The Kings and Pawns are always the standard FIDE Kings and Pawns, but there is a list of standard armies that are approved for tournament play in Chess (as opposed to Chess Variants) with different armies.
The choice of armies may be made by negotiation, by assignment (assigned by the tournament rules or the tournament director), by random choice, or by secret/simultaneous choice; this list is intended to name all the possible ways rather than to forbid any methods not mentioned.
The rules of this game permit this, but it is legal for the rules of any particular match, tournament, league, ladder, or friendly game to forbid it.
If same-army play is forbidden, then it is the player of the Black pieces who must break the tie, either by choosing (freely or randomly) a different army or by declining the choice and forcing White to do so. In other words, if both players get the same army but may not play a same-army game, Black has the choice either to choose another army or to keep the army he already has and force White to choose another.
In one case, Castling is different. When the piece on a1 or a8 is a colorbound piece, Castling must be done by moving the King 3 squares (to b1 or b8) and hopping the other piece over it (to c1 or c8). This is not optional.