Could someone explain how the price after ICO on the exhanges is decided? Is it up to the exchange to decide what the start price should be? I understand it then changes proportionally with its market cap but I don't understand how/who decides if each coin is going to be worth 1.00$, 1.10$ or 1.20$ when the coin is listed.

Also, what is the difference between pre-sale and public crowdsale?