From dictionary.com - linked from deal
a.the distribution of cards to the players in a game.
b.the set of cards in one's hand.
c.the turn of a player to deal.
d.the period of time during which a deal is played.
From poker hand
the 5 cards held in a game of poker
All the above is readily available using the Dictionary and thread title search at the top of this forum.
Poker hand does not mean deal. Poker hand refers to the cards dealt to one/each player, and the amount differs from game to game. Texas Holdem deals 2 cards to each player and other games like Stud deal 7 cards.
Metaphorically, there is a saying that you have to "play the hand you've got" (play the hand dealt to you by God) which means don't wish for things you don't have, make the most of what talents you do have.
Deal with respect to poker is a verb. However, it is possible that "the deal" could mean the set of cards dealt collectively... as a set.