Yes, you definiately have fresh/soph/junior/senior status, which is based on two things, one how many years you've been there and two how many credits you've earned.
How it is interpreted (socially) is usually up to you. For instance, I was a "6th year senior" when I graduated. As far as the school and anything technical/financial/academic is concerned, your standing is based soely on the # of credit hours you have. So if you have to maintain a 2.5 GPA when you are a junior, they don't care if you have been there 3 years, it's just the # of credits you have.
At many colleges, it isn't unusual to finish your bachelor's degree in more than 4 years, especially if they have co-op or internship programs etc. Or if they have a lot of CS majors who play games too much.