The primary difference at the undergrad level between physics and engineering physics, at Cornell at least, is that physics is in the College of Arts & Sciences while A&EP is in the College of Engineering. There's a lot of overlap between the two, all the way through to Physics 410, the senior lab course.
The primary difference between engineering physics and other engineering classes: A&EP is a lot harder, but in a way a lot easier. Physics majors learn fundamentals, engineers learn details. You probably will not come out as well-versed in structural engineering as will an ME major or circuit design as will an EE major (just to pick a couple). What you will have is a deep and thorough understanding of the physics that guides structural engineering and circuit design. Learning that detailed stuff is easy if you know the fundamentals. Another difference: the math they taught engineers was inscrutable to me. Physics and A&EP majors take real math classes.