git fork - creates copy of existing repo separate from the existing repo and its original creators. Lets you make independent changes without having to update original repo.
git clone - copies existing repo to local machine and allow you to work alongside creators of repo.
git branch - creates a branch inside a repo which allows people on the branch to make changes that are only visible in that branch. any one with access in the repo can also hop on that branch and make/view your changes. Branches also make it easier to work at the same time among multiple members, since multiple pushes on the same branch could cause problems for the repo.
Git fork is best used when you do not want to work alongside people in the repo, or want to individually work on a repo. Git clone is best used when you want to work alongside other creators, and want them to see your changes. Git branch is used when you are apart of a repo, but want to make independent changes that you might want to test before merging to the main branch.