All the expression below mean the same as "to fire someone". Except: A)To sack B) To lay off C)To make someone redundant D) To retire.
Making someone redundant has a very specific and legal meaning in British English, though the gist of it is, I think, the same as "lay off" in American English. Both refer to someone losing their job because the job no longer exists - the employer has shut down a project, scaled down a department, runs fewer shifts, etc. Making someone redundant doesn't require any cause, but there are rules about when and how it is done.
Firing someone generally suggests they have done something wrong, and that you, the employer, found the most appropriate way to deal with it was to end their employment.
All of these concepts are covered by to dismiss. Someone who's been dismissed from their job has lost their job, but it says nothing about why.
You can retire someone or something, but usually only something other than yourself. You will hear people talk about retiring a server or a piece of software. In terms of employment, people usually just retire, the verb being intransitive.