Both geminus and gemellus seem to have similar meanings: twin-born, born together, twins. Is the main difference between these two words how they were used, or did they have additional meanings that further separated them? There is a note for gemellus that seems to indicate it was used more in poetry.
This is the sort of question that dictionaries of synonyms were essentially created to answer. As this kind of dictionary seems to have thrived in the eighteenth and nineteenth century and somewhat withered since, they are all older texts. Let us see what we can find:
- Jean-Baptiste Gardin-Dumesnil published a dictionary of synonyms in the 18th century in French, which was widely adopted and translated. The English translation by one J. M. Gosset (1819) tells us: Geminus, twin, double, equal, or like. Gemellus, that is in pairs. (Excerpted from the full entry by me. This is a translation with additions, but in this case adds nothing to the French original.)
- The German translation of Gardin-Dumesnil's work by L. Ramshorn, 1831, is considerably extended and informs us: Geminus duplicate by birth, twin; therefore similar, equal, insofar as two things are of the same kind or are identical in their central characteristics. Gemellus born at the same time, belonging together like twins, poetic, expresses even more strongly the mutual relationship. (Excerpted and translated by me.)
Please see the linked full entries for various usage examples from ancient authors.
Note that morphologically gemellus is the diminutive of geminus. The latter is, so to speak, the original word, and it is much more frequent. Gemellus on the other hand is a derivation which is comparatively rare. In summary it is probably fair to say that:
- geminus is the humdrum prosaic everyday word for talking about actual twins and things that are closely linked in pairs, and (like English “twin”) it can also be used to talk about similarity and closeness in a wider sense; and
- gemellus is a more fanciful locution, mostly found in poetry, less suited to express the simple fact of a twin birth or close similarity, more likely to express pairedness and belonging-together of two things.