Metropolitan Toronto merged with the former City of Toronto, York, Etobicoke, North York and the Borough of East York to form the (current) City of Toronto.
The Greater Toronto Area is just a name for Toronto and its suburbs really. It isn't any official structure. The surrounding regions (Durham, Halton, Peel and York) are the upper tier municipal governments with lower tiers beneath them (Duham has places like Ajax, Pickering, Oshawa; Halton has Burlington and Oakville; Peel has Caledon, Mississauga and Brampton; York has Vaughan, Richmond Hill and Markham). A lot of the times we hear references to the the GTAH which is the GTA + Hamilton (because Hamilton is part of a separate census area, which includes Burlington).
A term that I think is older is the Golden Horseshoe, which include Toronto and Hamilton but I'm not sure where it ends (Niagara?). A term I dislike is "Greater Golden Horseshoe", which in my opinion sounds pretty stupid.