MGQ is Monster Girl Quest and MGE I THINK is Monster Girl Encylopedia.
you thought correctly. MGE is the Monster girl Encyclopedia.
to add more info to both games;
Monster Girl Quest is rather grim in its setting, the girls there will kill humans or mistreat them and lean more towards monster than girl, in terms of personality.
Monster Girl enceclopedia is softer in comparison, the main setting deal with tons of monster girls roaming about looking for a husband, and despite their voracious lust, they'll love their human and ultimately want to make them happy, therefore the monstergirls here lean more towards girl than monster.