There is a difference, actually, although its really behind the scenes and it doesn't make a difference to the students.
A school is generally headed by a Director. It is larger than a department (which is headed by a Chair). Larger than a school is a college, which is headed by a Dean. Whether something is a department or a school or a college depends on enrollment and funding and size of the faculty, etc. It usually goes Departments are in Schools which are in Colleges which are in Universities.
I say usually because sometimes there really is no difference and its just a name, and I think this is more likely for medical schools, which don't seem to fit the pattern. However, they may decide if its called School of Medicine or College of Medicine based on the same factors above, namely the size of the department.
At my school, though, our Computer Science department used to be just a department in the College of Engineering and Computer Science, but it grew so big (students majoring in it, faculty teaching it) that they made it into the School of Computer Science.