What is an owner in Yu Gi Oh?

Answer 1

The Owner of a card is the person who brought it to the game in their deck. Ownership of a card determines which graveyard the card goes to, whose hand it will go to when 'returned to hand', etc. While control of a card can switch, ownership does not, so even if an opponent takes control of a card, it will go to its owner's graveyard when destroyed.

'Token' monsters are summoned during the game and are not part of a deck. The owner of a token is the owner of the player who activated the effect that summoned them. Therefore if player A uses Ojama Trio, then Player B is the controller of the tokens, but Player A 'owns' them. Thus if 'Remove Brainwashing' was used, the tokens would go to Player A's control, even though he never controlled them before.

Black Garden is a little more complicated. Black Garden itself is always owned by the player who brought it to the deck, but the owner of the tokens it summoned is the player who triggered it. So if Player A is Black Garden's owner, and player B summons a monster, Player B 'owns' the token summoned to Player A's side of the field.

Lastly, Ownership alone does not entitle you to tribute a card or make decisions for it, to do that you must control it. Once you lose control of a card, even one you own, you can no longer do anything with it. So in the above example, even though Player A owns the Ojama Tokens he summoned under Player B's control, Player B is the only one who can change their battle positions, declare attacks with them, use them as cost payment (they can be 'sent' as a cost, by cards that do not require tribute), etc.