How does a poker odds calculator work?

[Constantinos]

How does a poker odds calculator calculate the probability for a specific hand to win against another hand or hand distribution like example PokerStove does?

Does it simulate the hand with the selected hands or does it use a special algorithm?

If I for example want to calculate the probability of QQ winning against AKs, does it then simulate:

Case 1: QQ vs AKs, simulates the hand with a flop, turn and river and sees which hands win (or split) and makes the simulation for example 1 million times to get an accurate probability value?

(PokerStove says 53.951% vs 46.049%)

Case 2: QQ vs AK, same procedure as above.

(PokerStove says 56.758% vs 43.242%)

Does it then combine the probabilities? In other words in the QQ vs AKs case it said that QQ wins 53.951% of the time, which means in 100 000 games it will win 53951,
and in the other case with QQ vs AK, QQ will win 56758/100000 times.

Conclusion: QQ wins against the hand distribution AK or AKs 53951+56758 = 110709 / 200000 times, which gives a probability of 55.354%.

The reason why I'm asking how to calculate the probability is because when I run the simulation QQ vs (AK or AKs) it gives the probability 56.056%, while my calculation gives 55.354%.

Am I doing the calculation correct? Thanks in advance!