In the peer reviewed Stanford Encyclopaedia of Philosophy on The Definition of Morality it indicates the two related problems by noting that:
Kant, in accordance with the German word “moral” that is used to translate the English word “morality,” regards morality as applying to behavior that affects no one but the agent, but most of the behavior that he discusses is behavior that affects other people. Hobbes, Bentham, Mill, and most other non-religiously influenced philosophers writing in English limit morality to behavior that, directly or indirectly, affects others.So we could say that religious morality is intra-personal or internal morality and its focus is on behaviour that only affects the agent, whereas secular morality is inter-personal or external morality and its focus is on behaviour that affects other people. Given possible prejudices provided by such qualifiers as "religious" or "secular" I will use the more neutral and more explanatory labels of "internal" or "external".
These are the two inter-related problems of morality (or sub-problems of "the" problem of morality, if you will). It might be possible that a solution to the question of an internal morality might successfully apply to someone who lives alone on an island, in isolation from others and never interacts with other people. However this is not the world we live in nor is it the world that is of moral concern to anyone. One can collapse the two problems into one, but only at the unjustified cost of obfuscation. Better to make the distinction clear. How can it not be obvious that a solution to one problem will impinge on the other and vice versa?
Of course, different approaches might prioritise one over the other, as an argued better solution to both but this is only a matter of emphasis and does not justify exclusion of the other sub-problem. To assert, as is often done by moral subjectivists, moral relativists and ethical egoists, that only one exists - that of an internal morality - and that is all that matter or can exists, is to change the subject, it is to fail to address and to provide a solution to "the" problem of morality, which necessarily must incorporate and acknowledge both sub-problems to have a chance of providing a possible solution, let alone a plausible or cogent one.
I wonder, is anyone who wishes to discuss morality with anyone else, through the mere act of so doing, is tacitly confirming that morality is not just about one's intra-personal relationship with oneself? If so, surely if they proceed to, at the same time, (fallaciously) reduce, collapse and define away the dual (internal/external) sub-problems of morality to just that of internal morality, have they not refuted themselves?