a character actor tends to be(stereotypically)- not always- someone that is not considered handsome/beautiful in a typical conventional way(tho appearance or beauty has little to do with it actually, more of how they are perceived, or categorized by casting people, etc.) yet by wont of their skill/talent and craft deliver dynamic and unique performances. They are usually 'scene-stealers', in best way, making scenes come alive in a way they would be humdrum without their presence.They aren't always in lead roles- but the iconic character actresses and actors 'break the mold' of a supposed ideal image of a performer- like a tom Cruise or Redford, Newman - and reinvent what an actor can look like and what types of stories are told about what types of characters...
Ernest Borgnine, Jackie Gleason, Dustin H. are some examples. Paul N., was not a character actor early in his career but has transitioned gracefully ( it seems) into more character acting as an older guy.
The ones I listed above actually broke out of being a character actor and showed that could also play leads and carry a film. Phillip Seymour Hoffman is a recent example.Shirley Maclaine has also become more of a character actress in later years, tho it could argued that there are far too few interesting lead roles for women, and if one doesn't begin accepting "character type roles', lead or supporting , actresses wouldn't get any work....And often character roles are the best written- tho not as well paid (yet compensated at awards season).
Method acting relates to Konstantin Stanislavsky, a Russian actor , director, and writer that has written a collection of important acting books, in which a "method" of acting , of approaching and preparing for a role is described, as he tells the story of doing it w/ his troupe/s - As I recall one of them at least. This was the Method of acting taught by American students of Stanislavsky, such as Stella Adler ( Brando's teacher) & Lee Strasberg (who ran the Actor's Studio, a renowned school in NYC, where Newman, Woodward(?), Marilyn M.,
among others, studied).
Someone who is a "Method actor", can be a "character actor"... I can't really describe the Method as such as I'm not one. Actors have diferent techniques and approaches... then again, some don't, and still get parts...! Good character actors can often get more work, potentially, because they don't play just one type of character - as 'leading' men/women sometimes do .... And even when the role is not a big one you pay attention when they are on screen because their work is riveting...