Does the multinomial coefficient create combinations or permutations? I am looking at this formula

I just want to make sure I get it. For example, if I want to split a fifty-two card deck into all the possible combinations of four, thirteen card hands, then I get:
$$\frac{52!}{13!\cdot 13!\cdot  13!\cdot  13!} = \frac{52!}{(13!)^4}$$
My question is does this create combinations or permutations? Does this create all of the possible groupings of 13 cards per group or does this create all the possible orderings?
 A: In short, this counts for the number of possible combinations, with importance to the order of players.
Let's assume the first 13 cards are dealt to player 1, cards 14-26 to player 2, 27-39 to player 3 and the last 13 cards to player 4. We have 52 cards, so there are $52!$ possible permutations. For the sake of argument, assume that player 1 got the full set of hearts, player 2 got clubs and so on.
It does not matter whether the first card dealt to player 1 was queen of hearts or 4 of hearts, the only thing that matters is that he got all of the hearts. That is, the inner ordering of the hand he got does not matter. He was dealt 13 cards, there are $13!$ possible permutations of these cards, that's why we divide in $13!$. for four players we divide 4 times, hence the number of of possible combinations with importance to the order of players is $\frac{52!}{13!\cdot 13!\cdot  13!\cdot  13!} $.
Now, if we don't mind which player gets which hand (with the same example we don't mind if player 1 gets full set of hearts, clubs, spades or diamonds), then we need to divide the previous result by the number of possible permutations of hands, which is $4!$.
So overall, the number of possible groupings of 13 cards per group (with no importance to group order) is
$$\frac{1}{4!}{52\choose {13~13~13~13}}=\frac{52!}{13!\cdot 13!\cdot  13!\cdot  13! \cdot 4!}$$
A: Your equation counts the number of combinations of 13 card hands. Note that it  differentiates between the hands, so it counts the number of possible hands dealt to 4 players where you care about which player got which hand.  This is not the same thing as the set of hands in which the hands would need to be unidentifiable.
