I think OP that your question about applying to both and related options has been nicely answered above. I would recommend you and those interested just seek to fully understand the differences in NROTC experiences MO V NO. In short it is not fully the same training or standards.
Read the differences in Marine v Navy option requirements:
Physical Requirements;
https://www.nrotc.navy.mil/physical_requirements.html
Academic requirements:
https://www.nrotc.navy.mil/acad_requirements.html
At a high level, MO marines at least in the programs I am most familiar with, have a far more grueling physical demands during their training. Talk to a NROTC buddy about 20 mile weekend hikes? Yes from MO, not necessarily for NO. And the NO folks have more academic demands with more calculus/ physics, I believe. Not that the NO option is easy physically by any stretch - just as a point of fact the MO option path is physically harder.
Service career wise, one of several appealing aspects of MO is "guaranteed aviation". At NSI, some cadet candidates were pitched this from a Marine leader presentation. Which means if you qualify and pass through the gauntlet of physical and ocular exams, and want to, you can serve in aviation (others please clarify more specifically as desired). For NO there is no such program/ guarantee... . And there are both fixed and rotary wing pilot opportunities in both NO and MO paths. But I think the majority of MO pilots statistically are rotary wing. (Please correct / add if those reading have more data).
I think at Cortramid summer training, NO scholarship track cadets spend a week with the marines, subs, surface, and aviation. If they love the Marine experience and find a "home" there, it's my understanding they can change focus in the remainder of their training, and pursue a path to serve as a marine officer in their commission.
https://www.nrotc.navy.mil/summer_cruise.html
There is a great camaraderie in the unit that for my DS no one cares who is or isn't what option. Most of his new buddies are MO. But I'm not sure that's the same everywhere.
Good luck.