I am a graduate student in Applied Physics program. The difference between Applied Physics and Engineering Physics is the following:
1. Mostly, Applied Physics is offered as a graduate degree, student in Applied Physics consider themselves as Physicist. Engineering Physics is mostly offered as an undergraduate degree, students in Engineering Physics often are more interested in Engineering problems.
2. Applied Physics is, in some schools, with the Physics program and department or at least in the school of science. In some schools, Applied Physics is in School of Applied Sciences. Engineering Physics is mostly in the School of Engineering.