I have seen one explanation about the difference between discrete and combinatorial optimization problems in such a way that "all combinatorial optimization problems are also discrete optimization problems but the converse is not true" [1].
I am not aware of the existence of such a problem. Also, looking at the literature, from vehicle routing to the scheduling problems, all of them are discrete (of course, some of them are mixed-integer). Could you enlighten me about how it is possible for a problem that is discrete, but not combinatorial?
[1] https://link.springer.com/chapter/10.1007/978-1-4613-0303-9_3