What are the metal parts of a boot where the laces are meant to go called? There are the circle parts and the hook parts. Do these have a different name each, or do they have the same name?
The Weinbrenner Shoe Company calls them hook eyelets and set eyelets:
For shoes and other clothing and accessories, eyelet is the common term:
noun [countable] a small hole in cloth surrounded by a metal ring, for putting a string or rope through [Macmillan]
The more generic term is grommet, though in my experience this usually refers to a larger hole as might be used for a sail or tarpaulin.
Definition from the Collins English Dictionary:
An eyelet is a small hole with a metal or leather ring around it in cloth, for example, on a sail. You can put cord, rope, or string through it.