what's the difference?

I don't think that there are firm distinctions. A character actor is someone who is usually in a supporting role, and the role is usually enhanced in some way. So a supporting actor would be a butler, but a character actor would be a snooty British butler. So a character actor specializes in these smaller, enhanced roles.

I think some confusion arises because, in comedy, at least, a lot of actors play essentially the same enhanced character over and over again, and they become identified with that sort of character - Vito Scotti, Burt Mustin, Kathleen Freeman, Reta Shaw, Bernard Fox - and people mean these sort of people when they say "character actor." But I think the term applies to anyone who plays a lot of smaller enhanced roles, even if it's not always the same type of role.

I\ But I think the term applies to anyone who plays a lot of smaller enhanced roles, even if it's not always the same type of role.

Yes, they have the versatility to play lots of different roles. In the 60s on Leave it to Beaver Wendell Holmes played a tipsy house painter, and a few seasons later and earlier played different teachers. Just one example.

Sometimes they become typecast for various reasons and become go-tos for certain kinds of roles.

On a comedy series, a lead actor or supporting actor is someone that would be a regular performer and is seen every week in one specific role. Character actors are guest stars played by a professional group of actors whose faces may or may not be familiar but their names are virtually unknown except to regular classic TV viewers. The roles they play depend on the personalities of the actors that viewers tend to associate with specific roles. For example, Charles Lane always tended to play grouchy Scrooge-like authority figures while Paul Lynde was cast in more outrageous screwball roles. It depends on what you're looking for. In the early days of TV, there was always a good number of character actors that you can depend on for any role on any show and seeing them at work always seemed to make those shows better.