alter

Alter, altera, alterum belongs to the small pronominal group that takes genitive singular alterius and dative singular alteri in all three genders, alongside unus, solus, totus, ullus, nullus and alius. Everything else declines like bonus.

The distinction that matters is arithmetic: alter is the other of exactly two, alius is another out of many. Alter also does duty for "second" in a sequence, and doubled up it splits a pair, alter... alter, "the one... the other". Watch alterius, which is shared with alius, whose own genitive alius is avoided in practice. The word is also the source of the Romance ordinary word for "other" - French autre, Spanish otro, Italian altro - so the everyday descendant comes from alter, not from alius. English took alternate, alternative, altercation and, through late Latin alterare, "alter" itself.