[gcruse]

" equivalent of their president!! "

Not exactly. A president is head of state. The Queen in the head of the British state. The PM is what the name implies. The prime minister of Parliament.

[DustyMoment]

Not exactly.

Yes, exactly. The queen's position is ceremonial, she has no official government responsibilities. When the Parliament was created (I think by the Magna Carta), the royalty basically lost most or all of their formal duties related to governing the people/country. Since that time, they have given up any remaining responsibilities they may have had. All they do today is perform ceremonial functions.