Forking creates an entirely new repository from existing repository (simply doing git clone on gitHub/bitbucket)
Forks are best used: when the intent of the ‘split’ is to create a logically independent project, which may never reunite with its parent.
Branch strategy creates a new branch over the existing/working repository
Branches are best used: when they are created as temporary places to work through a feature, with the intent to merge the branch with the origin.
More Specific :- In open source projects it is the owner of the repository who decides who can push to the repository. However, the idea of open source is that everybody can contribute to the project.
This problem is solved by forks: any time a developer wants to change something in an open source project, they don’t clone the official repository directly. Instead, they fork it to create a copy. When the work is finished, they make a pull request so that the owner of the repository can review the changes and decide whether to merge them to his project.
At its core forking is similar to feature branching, but instead of creating branches a fork of the repository is made, and instead of doing a merge request you create a pull request.
The below links provide the difference in a well-explained manner :
https://blog.gitprime.com/the-definitive-guide-to-forks-and-branches-in-git/