I don't disagree with you, being asked for a resignation and being fired are often very similar, but they have important legal distinctions that any employee should consider when faced with this choice. Even though it seems like a meaningless distinction.

If a regular employee "quits" rather than being fired in most jurisdictions, they do not collect unemployment. If Sessions resigns rather than forcing Trump to fire him, his replacement process is legally different.

In both cases, the person is trading certain things for a good relationship with their former employer. Jeff Sessions of all people is not under some feudalistic pressure from his boss to play the game. Jeff Sessions will be fine no matter what happens to him. Jeff Sessions could have had as much backbone to say "no, fire me" as he felt like. Trump has absolutely no leverage over him.