When an employee severs the relationship it is called “resigning”. This makes me wonder why the difference in language and if it’s part of the power play whereby companies seek to frame the relationship as sponsor/beneficiary rather than straight contract (which is what it is).
But also, as a practical matter, most "bosses" (line managers at least, not sure how true this is further up the org chart) in IT can't actually fire their reports. /They/ would be fired /themselves/ if they did. Instead, they are expected to "manage out" unfavored employees by just giving a few quarters of bad reviews, performance plans, write-ups, etc. until they start interviewing elsewhere and leave on their own.
However, I don't see any power play in the words themselves. An employee being fired and an employee resigning are different concepts, and different concepts get different words.
You could read something into the word "firing". But don't most companies avoid that word in any case, in favor of "letting go" or "dismissal"?
Firing is a slang term that would tend to be used by an unsympathetic press. The slang equivalent would be quit which has a similar strength.