According to Vine, allos and heteros

‘have a difference in meaning, which despite a tendency to be lost, is to be observed in numerous passages. Allos expresses a numerical difference and denotes “another of the same sort;” heteros expresses a qualitative difference and denotes “another of a different sort.” Christ promised to send “another Comforter” (allos, “another like himself,” not heteros), Jn 14:16. Paul says “I see a different (AV,”another”) law,” heteros, a law different from that of the spirit of life (not allos, “a law of the same sort”), Rom 7:23. After Joseph’s death “another king arose,” heteros, one of quite a different character, Acts 7:18. Paul speaks of “a different gospel (heteros), which is not another” (allos, another like the one he preached), Gal 1:6,7. See heteros (not allos) in Mt 11:3; Acts 27:1; in Lk 23:32 heteroi is used of the two malefactors crucified with Christ. The two words are only apparently interchanged in 1 Cor 1:16; 6:1; 12:8-10; 14:17,19, e.g., the difference being present, though not so readily discernible.’

Bill Mounce notes that the distinction between allos and heteros held in classical Greek, it was not always present by the time of the NT.  Neverthess, he agrees that it is preserved in a number of places.  For example, in 1 Tim 1:3 ἑτεροδιδασκαλεῖν the context indicates that Paul is referring to teaching that is essentially different from his own.  That particular word occurs elsewhere only in 1 Tim 6:3, and appears to have been coined by the apostle himself.