Sort of

For most toilets there’s universal fittings that will work just fine, you may need to adjust them a little bit, but they’re made to be adjusted, and they’ll work just fine with most toilets.

If you have the original factory parts in your toilet, they may not be adjustable, and if you tried to swap them into another toilet they may not fit/work in other brands/models, or they may kind of work, but maybe not quite right.

There are a handful of brands that don’t tend to play well with the universal fit parts, I want to say Kohler is one, and if you go to a hardware store, most likely they’re going to stock the universal parts, then a couple of the most common oddball brands.

There’s also of course some weird toilets that are just totally different- pressure assisted flush, composting or incinerator toilets, etc. that aren’t even working on the same principle as most toilets, but I think the odds are that if you have one of those, you know that already.

Also I haven’t played with any toilets that were manufactured that way, but I did retrofit one of my toilets to be a dual-flush. Those kits seem pretty universal, but probably double-check before trying to put them in an oddball toilet.