Terminology:

1. Overlap: Spacings that overlap with one other.
2. Regular spacing: Spacings that are fully separated from one other which doesn't forms any overlap.
3. Combo count: The number indicating its order inside one complete combo.

Types of Overlaps - Combo Counts

1. Objects at the same coordinate

1-1. Perfect overlaps
Objects that overlap perfectly each other to the extent where they do not form a stack. This setting can be done by adjusting the "stack leniency". A perfect overlap displays zero tolerance of difference in placement which can be appropriate in several situation.
1-2. Stacks
Stacks happen when when objects are placed at the same place, and when the stack leniency is high enough. The auto-stack is done 4 axis left and above each from the final object.

2. Objects at a different coordinate

In this section, objects with a different coordinate that forms an overlap each other will be analyzed. The key tool here that I will be using as a standard of analyzing things out will be the combo counts. To avoid confusion with the term, a combo count is the number that appears at the hit circle which indicates its order inside one complete combo.

I won't be covering about manual stacks here since it technically has less difference in analyzing its type with "stacks".

2-1. Combo count invisible
An overlap can never happen on a single object. It needs at least 2 objects to make something overlap. This case, the combo count of (2) is completely overlapped with the first object resulting in an invisible combo count. This is about more than half of the circle being overlapped each other approximately.

Eventually, stacks and complete overlaps would be included under this category since they do not have a visible combo count along the overlap. There are just additionally classified due to their extra attribute.
2-2. Combo count partially-visible
The combo count of the stacked object has became visible, yet to reveal its full number. It is not fully visible.
2-3. Combo count fully-visible
The combo count of the stacked object is fully visible yet forming an overlap.

Misc. Hitcircleoverlay overlaps?
I'd like to introduce an extra concept which is an overlap done between hitcircleoverlay. Unlike the previous overlaps, this is an extremely rare overlap to happen since it is only the hitcircle"overlay" that is overlapping, while the "hitcircles" are completely separated.

Even I have classified this as a special category, what do you think about this overlap usages? Could this even be considered as an overlap? Or is this just a subtle placement choice that is neither forming an overlap nor a regular spacing?

Types of Regular Spacings - Follow Points

This section, objects with a regular spacing will get analyzed. The key tool here that I will be using as a standard of analyzing will be the follow points. By the existence of the follow point or the placement of the follow point, the spacing could get categorized into several types.

1. Objects without a displayable follow point

1-1. With an extra space
When the regular spacing is close enough, there is a certain point when a follow point no longer gets displayed in the playfield. As the example below, no follow point was created while there was a sufficient space between (1) and (2).

Since the follow point display is inconditional in circle size, the smaller the circle, the bigger that spacing would be.
1-2. Witout an extra space
It is also possible to place objects close enough so nearly no space exists between the two. Even it the concept of having no follow points is similar with the above, be aware that this difference actually lead to a different kind of a spacing.

2. Objects with a displayable follow point

2-1. Follow point unbalanced (leaning behind)
The spacing which contains a visible follow point that is leaning to the following object. Perhaps the actual spacing may look similar with 1-1, but please be aware that the existence of a follow point definitely created a difference.
2-2. Follow point unbalanced (leaning forward)
The spacing which contains a visible follow point that is leaning to the preceding object. Though it has a similar feeling with 2-1 in that the follow point being placed unbalanced between those objects, you can also keep an extra space.
2-3. Follow point balanced
And finially, this is a spacing which contains a visible follow point that is completely balanced between two objects. Unlike the previous two spacing concepts, since this is having a balanced placement, it provides a visually stable effect.
One of the interesting feature of this balanced follow point spacing is that this corresponds with a back and forth pattern nicely. Seen from the following usage, creating a back and forth pattern creates two follow point at the same spot, resulting in another visually stable setting.
Remember, all follow point spacing concepts above can also get applied to when there is more than one point!

Why is this important?

When mapping things out, you will confront sections where you want to place objects in a "consistent" spacing. Maybe some would rely on distance snapping to achieve the goal, but some may not! For those who are not big fans of distance snapping, they can still use a consistent spacing by applying this concept. Placing stuffs actually consistent as you intended is really important because spacings are one of the most basic elements inside a map.

This analyzing tool is also effective to detect spacing errors when you mod maps. Take a look at the following image.
If you fully understood this concept, you should be able to detect the spacing error immediately without even needing to click (2) to fix the actual distance snapping value. The spacing is jump obviously different.

Questions

Q. To how much extent do I have to detect as a spacing error?

This would be completely depending upon what map you are modding at. There might be very strict mappers who does not want a single spacing error in their maps. For those, mentioning even a small difference according to the spacing types I've provided (not by 0.02x difference) could help improving the map's detail no matter how nazi it may look. There might also be mappers who aren't really that strict to distance snappings. For them, mentioning some crutial inconsistency of the spacing type would be just enough. Those should be able to detect without even applying this method.

Q. But I use a linear follow point! Would the analysis method you provided work for me?

Unfortunately, this method does not really apply that much after "displayable follow point" section. This is because the linear follow point skin being self-balanced itself. This feature of the skin reduces about 4 spacing categories into 2. Visible vs Invisible.
The above image is having the exact same placement that I have provided right before. Is it easy enough to detect its inconsistency? No it didn't, while that inconsistency wasn't giving any positive influence in terms of beatmap quality. Using a linear follow point skin makes spacing issue less sensible, and you should use the skin on your own risk.

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Thanks for your time! If you know an extra method to analyze spacings, also sharing your idea here would be highly appreciated!
Also I'd like to make sure this guide to be about basic spacings.

I hope you guys to get the difference between spacings, and could select the one that best fits with your mapping~

Common Distance Snapping Error after SV Change

There is a very ordinary looking stream here. At glance, it has a consistent spacing and in reality, it is.



However what happens if there is a slider velocity change at (5)? In this example, I have used a 0.8x sv multiplier and the resulting was like the following.
As you can notice, the distance snapping value displays an inconsistent number while the actual placements are visually consistently spaced. Nothing has changed from the first stream, but the distance snapping is telling you "0.83x" and "1.07x".
After adjusting the placements to make the distance snapping value consistent to arround "0.83x", the visuals became inconsistent now. Not 100% sure about the inconsistent visual? Review the "2. Objects at a different coordinate" section at the above spacing analysis and you should be able to detect that the spacing concept has changed from "2-3. Combo count fully-visible" to "2-2. Combo count partially-visible".

This happens because the distance snapping function is based on slider velocity, and the modified sv also resulted in a modified ds.

The conclusion of this issue is about making your spacings consistent according to the visuals and actual movements, not according to the numbers.
If the stream wasn't enough, here is a clear example why you should be following the spacings of visual and movements. Remember not to just blindly following the distance snaps. I see such errors way too much in slider velocity changing sections, or bpm changing spots. These are especially fatal on lower diffs, so please don't make this kind of mistakes.

Nice guide! Good work

^ oh good to know. Actually I posted it with (4,4) since that was how the editor displayed stuffs, but I've saw some case of (3,3) so haha
That was why!