"What is the difference between Grommets and Eyelets?"
Well, that depends on the grommets and the eyelets you are comparing. They are basically the same thing. Some people say that eyelets don't have washers but that's not a fact of all eyelets...only of some brands.
Grommets and eyelets at typically made of some type of metal (though plastic do exist), they're typically a circular short tube with a "flange" (flat end).
I use them primarily for the back of corsets, they strengthen the holes that the lacing goes through. The tube of the grommet or eyelet goes through the hole from the "right side of the fabric", so you'll see the flange on the outside of the garment.
A washer looks a bit like the "flange" of the grommet or eyelet but without the tube. The washer goes on the "wrong side" of the fabric or on the "inside" of the garment. The washer keeps the grommet or eyelet secure during lacing and inhibits the grommet or eyelet pulling out of the fabric. Using fusible interfacing on the "wrong side" of the fabric also helps. Washers should always be used with grommets and eyelets unless the grommet and eyelet are just decorative.
Grommets are available in brass (gold colour), nickel (silver colour) and matte black (gunmetal). washers are included and match the colour of the grommet.
Eyelets are available in brass (gold colour), nickel (silver colour), antique brass, shiny black (made of aluminum), white (made of aluminum) and matte silver (aluminum). Washers are sold separately and are matte silver (aluminum). Aluminum does not corode when exposed to persperation which makes it a great choice for corsets that are worn alot or exposed to other moister.
It's important to note that grommets and eyelets are not universal in size. Meaning not all grommets listed as size #00 can be set with the same grommet setter. You need to have the grommet setter that was designed and engineered to set the grommet brand you have otherwise you risk a poorly set grommet or worse...a grommet stuck onto your grommet setter, which means your garment is stuck on to!