ok, this from www.dictionary.com
match /mætʃ/ Show Spelled[mach] Show IPA
1. a person or thing that equals or resembles another in some respect.
2. a person or thing able to cope with another as an equal: to meet one's match.
3. a person or thing that is an exact counterpart of another.
4. a corresponding, suitably associated, or harmonious pair: The blue hat and green scarf were not a good match.
5. Sports .
a. a game or contest in which two or more contestants or teams oppose each other: a soccer match.
b. a contest consisting of a specific number of sets: a tennis match.
6. any contest or competition that resembles a sports match: a shouting match.
7. a person considered with regard to suitability as a partner in marriage: a good match.
8. a matrimonial union; marriage: Neither family approved of the match.
a team match is a contest between two teams (definition 5a.)
But from now on, i will refer to a team match as a team match, a backgammon match as a bg match to avoid confusion.
tour·na·ment (tŏŏr'nə-mənt, tûr'-)
1. A series of contests in which a number of contestants compete and the one that prevails through the final round or that finishes with the best record is declared the winner.
2. A medieval martial sport in which two groups of mounted and armored combatants fought against each other with blunted lances or swords.
a team tournament will be a series of team matches (definition 1.) (although a team match could fit the definition of a tournament, it is not the best definition, it is one contest between two teams, not a series of bg matches between individuals)
league /lig/ Show Spelled [leeg] Show IPA noun, verb, leagued, lea·guing.
1. a covenant or compact made between persons, parties, states, etc., for the promotion or maintenance of common interests or for mutual assistance or service.
2. the aggregation of persons, parties, states, etc., associated in such a covenant or compact; confederacy.
3. an association of individuals having a common goal.
4. a group of athletic teams organized to promote mutual interests and to compete chiefly among themselves: a bowling league.
5. Sports .
a. major league.
b. minor league.
6. group; class; category: As a pianist he just simply isn't in your league.
a team league will be a set of teams organized to compete between themselves (definition 4.)
So as you see, there is no "radical re-definition" here, only a definition of thier use
so, i plan to have oranges (team tournaments), and apples (team league), so i don't want to call a pear (team match) an orange, or an apple.