For FUE, there are less restrictions since you don't have a continuous linear wound that is closed. Avoid contact sports for ~10 days. You can run after about ~3 days and lift weights ~10 days.
For FUT, you want to avoid exercises that will stretch your neck. So no heavy lifting for at least 2 months and you can do light weights ~14 days and run ~7 days.
As always, it's best to consult with your surgeon beforehand.