How similar is the Internet browser on the iPhone to the one on my computer?

I have been considering buying an iPhone. One of my primary interests is being able to browse the Internet. I was wondering though what browser the iPhone used and if there where any limitations it might have with accessing the Internet that my normal computer might not have. How would the iPhone Internet browsing experience be different than my normal computer browsing experience?

The most obvious thing would be the size of the screen and not being able to use your mouse. I mostly go online using the phone to check live cricket scores etc so there isn't much of a difference to me. But if you are looking to engage a lot with whats in the screen then it might take some getting used to