Since you said "some" of the endpoints, that means the internal API and the public API are already meaningfully different interfaces, in addition to having completely different user bases. Therefore, it's entirely possible that one may need to change in ways that should not have any effect on the other. So yes, it makes perfect sense to use separate version numbers for each API.
Just make sure that the way you expose these endpoints is sufficiently flexible that you will be able to make changes to the public API or the internal API without affecting the other, if you so choose. And you should have two completely distinct "public API declarations" (whether that means header files or API documentation or something else for your project).