Hi, here are pieces of the PED entries for the two verbs, various aorist forms given for each.
One major difference is the long vs short a that begins each verb.
Āgacchati Āgacchati [ā + gacchati, gam ] to come to or towards, approach, go back, arive etc.
I. Forms (same arrangement as under gacchati): (1) √gacch : pres. āgacchati D i.161; J ii.153; Pv iv.151; fut. āgacchissati J iii.53; aor. āgacchi Pv ii.133; PvA 64. — (2) √gam : aor. āgamāsi PvA 81, āgamā D i.108; J iii.128, and pl. āgamiŋsu J i.118; fut. āgamissati VvA 3; PvA 122; ger. āgamma (q. v.) & āgantvā J i.151; Miln 14; Caus. āgameti (q. v.). — (3) √gā : aor. āgā Sn 841; Pv i.123 (= āgacchi
Gacchati Gacchati [Vedic gacchati
aor. agacchi (VvA 307; v. l. agañchi). — (2) gam˚ in three variations; viz. (a) gam˚, in pres. caus. gameti; fut. gamissati; aor. 3 sg. agamā (Sn 408, 976; Vv 797; Mhvs vii.9), agamāsi & gami