Quit erases all the definitions (by quitting the kernel), but so does
ClearAll["Global`*"] (or other contexts). What's the difference in terms of variables in the notebook?
There are significant practical differences.
Quit does not "clear" anything, it instead restarts the kernel, i.e. resets it to the default state. There is a lot of internal state that changes during the session in ways that are different from creating new symbols or attaching definitions. So simply clearing (or removing) symbols won't reset the kernel. Examples include:
When you load a package, it does not only create its own context, it also causes
$Packagesto be modified
Symbolic results are cached (
ClearSystemCache) and will actually cause symbolic processing functions to return different results than they would in a fresh session.
pseudo-random number generator states change (and this also involves caching behind the scenes, which in principle affects memory usage)
Logins to various services (e.g.
SocialMediaData) may be remembered until the end of the session
Parallel kernels keep running,
ParallelNeedskeeps remembering "needed" packages,
DistributeDefinitionskeeps remembering what was distributed
A fresh kernel doesn't have all symbol definitions loaded. Using various symbols triggers loading definition and triggers loading packages.
These are just a few random but concrete examples that came to mind. This list is not at all meant to be exhaustive, it is simply to illustrate how many things get modified during a session. There are many more than these, very likely including many which concern the internal workings of Mathematica and we don't even know about (as they are not publicly documented).
This is all in addition to the difference between
ClearAll which people mentioned in the comments and which is also significant (e.g.
ClearAll won't help with shadowing but
In short, if you are having trouble with Mathematica, reset it fully by restarting the kernel, don't just clear your own definitions.