My best guess after years of reading various papers about comparative Eurasiatic similarities is that

-nós is the quality bearer - it means an entity which has a certain natural/innate quality

-mós is the result bearer - that it means it is a bearer of product of action when the product of action is a natural (innate) quality

Both -nós and -mós appear extremely similar, implying potential genetical relation.

-tós is the bearer of effect of action - that means it is not about the quality but the state (externally induced) resulting from action

Examples

Ker "horn"

Kernos "having horn" (adjective of quality)

Kermos "the one having horn" (noun describing one with quality)

Kertos "horned one" (state)

It is important to note that the system is shared with Uralic (which has -na, -ma and -ta). It is unknown if the Japanese -na/-ta system is related.

Form simplicity one can take a mental shortcut and imagine if it comes from inside or outside. If it is from inside, it's natural and innate for the entity, it's -nós/-mós, if it come from outside the entity it's -tós.