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?
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.