RCOOH + R1COH + H+ ---> RCOOCR1
RCOOCR1 + OH- (usually NaOH) ---> RCOONa + R1COH
so esterification uses catalytic acid, acid and alcohol to make esters
saponification uses at least 1 equivalent sodium hydroxide (or KOH) to make acid salt, alcohol
so they are opposites of a single reaction forwards is esterification; backwards is saponification.