Pacifist - During the pacifist route, you'll only see Muffet at the spider bake sale and after that, she wont fight you
Neutral - During the Neutral route, you will fight her and you can choose if you want to kill or spare. You will still see her at the spider bake sale.
Genocide - During the Genocide route, You will not see Muffet but you'll fight her.
Muffet's apperance is a purple kind of dress and she will hold Glasses and a book, If you defeat her in neutral or genocide her glasses will break.