Yea, everyone categorizes and records how they interact with people and differentiate them by race since it's easier to distinguish people like that on a basic level of sort of "mental taxonomy." That and everyone has different opinions based on how they interact with a certain race, even their own, usually passive or nothing remarkable, though- but I think we all do act a little differently around every race we come in contact with, which is, technically, racism.
But there's nothing wrong with that, it's human. It only becomes a problem when people put negative connotations along with their perceptions of a race or somehow think that a race puts someone lower than themselves or puts them at a disadvantage intellectually, etc. When you become a bigot, that is.
I admit that I do act a little differently around my Black, Indian and Hispanic friends as compared to when I'm with White people. But hell, I act differently when I'm with my friend and his Irish family compared to how I am with my Swedish family. Everyone does things like that, where they change themselves based on previous experiences with a different kind of people. Even when its not based on race, but just people you dont know very well. We're all the same species, but there are differences between us, but that's what makes us great, when we embrace that rather than try to think that "we don't see race" or that there is no racism.
TL;DR- Yes, but it's only human. Everyone sees race. Not a problem unless you're a bigot about it