When you create an abutting stencil, every part of the surface is painted once and only once. In an overlapping stencil, you can paint over previous colors.
The same image can be stencilized in an abutting or an overlapping way. But some images work better one way than the other. Here’s an example of stencilizing an image of a ladybug.

The color layers are overlapping. Notice how the black dots are painted over the big red body of the ladybug.
The same image could be stencilized so that no part of the surface is painted more than once. This is an abutting stencil of the ladybug.

When you stencilize the ladybug this way, there are problems that are illustrated in the video. But what it comes down to is that the red layer of an abutting ladybug stencil has a lot of bridges in it: the bridges that connect the masking material that keeps the dots from being painted red. (I encourage you to watch the vid for more detail on that.)
For this reason, I call an overlapping stencil that works like this a ladybug stencil: because ladybugs work best with overlapping stencils.
Ladybug = overlapping
But sometimes you want the layers of your stencil to be abutting. Take for example the image of a zebra. You could make an overlapping stencil of a zebra. Let’s see what that would look like:

That works great, as long as I want to paint on a white surface. But what if I have a black surface and I want to paint white stripes on black? The problem is that I don’t have white stripes; I have a white zebra-shaped blob. Now look at what happens if I make the zebra with the layers abutting.

With the abutting stencils, I can paint it on white or I can paint it on black and it looks great either way. If I try to get smart with the overlapping stencil and use the black layer to paint the white stripes, I end up with a weird color-negative look (especially around the eyes) which might be cool but it’s not what I was trying to do. But this stencil is not ideal, because–while you can paint just the black stencil on a white background with this stencil, you can’t paint just the white stencil on a background and get anything like a zebra. That’s why for the zebra you want an abutting stencil. With this stencil, you can also paint the white stencil on a black background and get a zebra out. (See the video for more details on how this works.) I call an abutting stencil a zebra stencil because the zebra works best with an abutting stencil.
Zebra = abutting (non-overlapping)
So to recap visually:

With an overlapping stencil, the order in which you paint the layers matters. That’s usually not a big deal, but it can get really complicated when part of your image is black dots on a red background and another part of your image is red dots on a black background!
Another thing is that, in the real world of the Stencilizer, we encounter relatively few ladybugs. That is, there are not so many cases when there are lots of discrete blobs of color A on top of a large patch of color B. Yes, it happens sometimes in faces (which can be a big deal), but the more layers you add, the less it happens.
The last advantage to non-overlapping (‘zebra’) stencils is that (as we see in the case of the donkey) they are more flexible when it comes to leaving out a background color. A non-overlapping stencil allows you to decide to change your background color to ‘the other color’ whereas an overlapping (‘ladybug’) stencil does not.
With an overlapping stencil, it’s important to know the order in which the colors will be painted, so that you don’t end up erasing detail that you really want. But sometimes an overlapping stencil is just what you want. Take, for example, the case of the ladybug. Here is what a stencil for a simple ladybug looks like when it’s abutting. And here’s what it looks like when it’s overlapping.
So, some online stencil makers create overlapping stencils (and there is only one order to paint the stencil). This academic stencil creator is an example. But in my stencil work I’ve found that I more often want an abutting (non-overlapping) stencil because it’s more foolproof, and allows me to have more flexibility in working with the image.
Get the zebra stencil. (Both include cut files.)