What is the formal definition of a TCG?
According to Wikipedia, they are one and the same.


  A collectible card game (CCG), also called a trading card game (TCG) or customizable card game, is a kind of card game that first emerged in 1993 and consists of specially designed sets of playing cards.


From Wikipedia the definition of a CCG (and hence TCG) is:


  Collectible card games (CCG) are generally defined as those where the player acquires cards into a personal collection or library, from which they create customized decks of card within the game's ruleset to challenge other players in matches.