The difference is that in Engineering Physics you have a mandated set of applied courses and, if the program is ABET accredited, you have a required design component. With a Physics degree, there is usually no design requirement and your electives are free to be whatever you like.
Someone with a Physics major can access the same jobs as an Engineering Physics major but the ABET accreditation of the latter might make it a bit easier to be considered for engineering positions.
Becoming a theoretical physicist is a long road and you have to be extremely dedicated to go through a B.S. and Ph.D. and then at least one postdoctoral position before getting a shot at the limited number of theoretical permanent positions. yes this is a daunting and long road but if you have the determination it is possible. You don’t have to decide right away. All physics B.S. degrees are basically the same and you can start by deciding if you want to go into graduate school once you are done with the B.S.