- is what you are legally obliged to do. Question is your morality.
About copying vs fork - depends on what you want to achieve. If it is meant to be soft-fork that is meant to be merged into mainline one day, then I would use GitHub Fork. If it is meant to be an implementation with different API and few other features - go with hard-fork.
For example of such project that hard-forked for adding few bells and whistles, while keeping a lot of patches - see NeoVim vs Vim. Of course you do not need to retain whole history in your fork, but you are free to do whatever you want, as long as you mention the original authors (at least legally).
