On the iPhone, the web browser is called Safari, just like on the Mac. This sameness is reinforced by the visual design of both applications. But in the new iPhone software, when they added a search icon, they did it on the left, instead of the right, which puts it out of sync with its desktop cousin.
I assume this was done because the search button that was added in 1.1.3 replaced the bookmark button on the left. I agree, though, that search should be on the right, like it is in every Mac application. In any case, I think the addition of the search button is a big improvement—some iPhone users had trouble remembering that you could tap on the location field to get to the search field.