Here's the official (sort of) version:
Milk shake - ice cream, syrup, milk mixed in a soda shop blender
Frosted - same ingred. but usually cheaper, and less butter fat, and mixed in a McDonald's or Wendy's machine. Usually comes out like soft ice cream
Malted - ice cream, syrup, milk, malt powder
Frappe - french term for thick milk shake usually in New Eng. Comes from the french term for partly frozen fruit drink.
Egg Cream - milk shake w/ a raw egg blended in. Really rich, but they're wonderful.
Float (ice cream soda) - Syrup, soda water ice cream mixed justuntil the dip still remains.
Alot of these terms are interchangeable depending on region, etc., so don't worry about the words, just enjoy the shake, float, malt, frappe. . . .