I plead ignorance to Canon batteries, but "different camera" doesn't have a lot to do with it.
I mentioned the EN-EL15 batteries. I've owned 4 different cameras that use these batteries-the D500, D600, D800, and D810. In fact, Nikon even swapped one of my old batteries when I got my D500(there was a weird glitch with the D500 draining some early EN-EL15s fast).
The D7xxx, D750, D780, D850, Z6(II) and Z7(II) also use these batteries. I'm probably missing a few. A lot of these are quite different cameras.
Before that, there was the EN-EL3e used in the D200, D300, D700, and a couple of others. It also made its way into the Fuji Finepix S5, although they will(annoyingly) only work with Fuji brand batteries or aftermarket batteries specifically made for that camera.
The same battery isn't a make-or-break for me, but it's a big plus when looking at a new camera.
I do have one regularly used camera that uses a different battery than my others and it's super annoying...