What is the difference between mange and manges?
They seem to be the same thing...
to expand on the conjugation, regular "er" French verbs (like "manger") are conjugated by dropping the "er" from the stem ("mang") then adding the following:
je (I) stem+e = je mange
tu (you) stem+es = tu manges
il/elle/on (he/she/it) stem+e = il/elle/on mange
nous (we) stem+ons = nous mangeons (manger is an exception because of the 'g')
vous (you) stem+ez = vous mangez
ils/elles (they) stem+ent = ils/elles mangent