"If you go now, we'll pay up your contract, and bonuses due, so we can get someone else in, whereas if you carry on, you'll get fired anyway in due course and won't get any bonuses because the team will keep losing"
You're fired (but we don't want to admit that publically, so if we give you alot of money to go away quietly we won't say anything more about your abysmal performance).
Its normally a financial compromise between getting in full what you are contracturally owed by your employer, and getting the sack and receiving nothing.
Hodgson for example MAY have been owed 2 years more money, but may have accepted 6 months and signed a 'compromise agreement' agreeing not to sue for wronful dismissal and just to go quietly.
I believe in football terms, our own Barry Lloyd was the first such casualty to be classed by the media as a 'mutual consent' departure when he left in 1993.
Fired (in all but name), but on terms that both agree and therefore no subsequent legal acion. I.e. "You're going, we may as well make it as painless for both sides as possible".
Same here. The equivalent for the rest of us, would be being asked to resign. It's less painless all round, and will probably involve a discuss and agreement as to your severence pay, as opposed to having to fight through a tribunal for it. Also, leaves you a whole host of options on your CV as to why you resigned.