In short, jo awase are kata where the two partners make the same movement,
That migth be a criterion in Iwama Ryu. But in other styles the movements of shidachi and ukedachi in awase exercises are most often not the same.
jo awaze and ken awaze is simply a type of exercises to practice timing, ma ai (=awase)
, ai (=awase)
kumi jo and kumi tachi are forms, paired kata, which simulate a fight.
To practice a solo form paired, can teach awase and helps to understand the movements of the form.
It is not called kumi tachi because there are often some "strange" situations which wouldn't make sense in a real fight, but teach something special here.