Yes the eggplant is related to zucchini.
The eggplant is in a way a zucchini but in an egg shape.
The reason eggplant is called eggplant is not because it has eggs but the eggplant is shaped like an egg so the eggplant is called an eggplant for that reason.
The eggplant is also a member of the genus Solanum and is related to the tomato as well as potato.
Eggplants do have a similar taste to zucchini but they do taste a bit different.
The eggplant is not really the same as a Zucchini but it is related to the zucchini and tastes nearly the same.