The difference is that 'Alliance' can be terminated (by toggling "Break Alliance" in the Foreign Policy screen to the left). In ' Team' this is not possible, so AFAIK you can´t attack your team-partner or impose a trade embargo on him.
'Team' can´t be created in-game, you´ll have to set it ("Relations") on the last starting-screen where you select your opponents.
Please notice any relations set better than 'Friendly' can´t be played as MV game. Because of this reason I´ve never played a game with that relation, but it would be interesting to know what will happen if somebody declares war on my team-partner? Is there the same screen as in alliance, or will I automatically join into the war?