These three commands have entirely different purposes. They are not even remotely similar.
git revert
This command creates a new commit that undoes the changes from a previous commit. This command adds new history to the project (it doesn't modify existing history).
git checkout
This command checks-out content from the repository and puts it in your work tree. It can also have other effects, depending on how the command was invoked. For instance, it can also change which branch you are currently working on. This command doesn't make any changes to the history.
git reset
This command is a little more complicated. It actually does a couple of different things depending on how it is invoked. It modifies the index (the so-called "staging area"). Or it changes which commit a branch head is currently pointing at. This command may alter existing history (by changing the commit that a branch references).
Using these commands
If a commit has been made somewhere in the project's history, and you later decide that the commit is wrong and should not have been done, then git revert is the tool for the job. It will undo the changes introduced by the bad commit, recording the "undo" in the history.
If you have modified a file in your working tree, but haven't committed the change, then you can use git checkout to checkout a fresh-from-repository copy of the file.
If you have made a commit, but haven't shared it with anyone else and you decide you don't want it, then you can use git reset to rewrite the history so that it looks as though you never made that commit.
These are just some of the possible usage scenarios. There are other commands that can be useful in some situations, and the above three commands have other uses as well.
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