I think my definition of cheap vs frugal is best explained with an example-
Cheap: Stays at a 2-star hotel because it's cheap.
Frugal: Stays at a 5-star hotel on sale for a 3-star price because it's good value (not necessarily the cheapest option)
Which one are you?
I am cheap with some things and lavish with others. And this can change depending whom I am with, or my mood.