1. We cannot return value to the Visualforce page i.e callback.
2. We can call the apex methods only from the class linked to the Visualforce page.
3. Action function cannot submit the form.

https://www.infallibletechie.com/2012/10/calling-controller-method-using.html

Remote Function:

1. We can return value to the Visualforce page i.e callback.
2. We can call the apex methods from any apex class.
3. Remote function can submit the form.

https://www.infallibletechie.com/2012/11/remoteaction-in-visual-force-page.html