Deactivating a player takes them out of future squad-selection eligibility without touching anything historical. Their existing stats, appearances and season totals stay exactly as they are. Use this for someone who's stopped playing but whose record you want to keep intact, the same way match history is preserved everywhere else on Dugout.
Removing a member from the club is the admin-side equivalent of someone leaving on their own. Use this for a person who's genuinely gone and isn't going to log in themselves to leave (see Leaving a club). It follows the same historical-data handling: their record isn't deleted, just detached from active membership.
One exception either way: a club's Owner can't be removed through either of these. Ownership has to be transferred first. See Transferring club ownership.