Is there a legal difference between termination and asked to resign?

Answer 1

We'd need more context really. In practice they amount to essentially the same thing, and being asked to resign is just a more honest form of constructive dismissal (which is where an employer makes the work environment so unpleasant that the employee resigns rather than continue to put up with it... for example, reducing their hours or scheduling them for awkward shifts).

Answer

Yes- If terminated, one can attempt to be compensated in the case of wrongful dismissal or, depending on the benefits offered by a company, take advantage of any severance packages. However, if you resign, you waive all right to take action against the company for your departure.

Depending on the grounds for being asked to resign, it may work in your favor (an employer is more likely to provide a positive referral for an employee who was "asked to resign" than "terminated") and so make finding another job easier.