Could someone explain what these refer to? Are these wheel sizes or types of bikes? Thanks.

Wheel sizes. Have you done any reading of what Sheldon has produced? It's a bookmarked link I have concerning gears, but navigate to all kinds of info from there.

Wheel size... kind of. 29er tires actually mount on 700c rims. In the case of 29er, it refers to a frame that can accept oversized tires. But yeah, check out Sheldon Brown's wheel sizing page.

The short story, though, is that 700 refers to the outside diameter of the tire... nominally, in millimeters. 26 and 29 are the same, except in inches.

don't bother trying to measure a tire or wheel in hopes of determining it's "size." as stated above, those numbers are NOMINAL sizes.

700c- road bikes, hybrid bikes, cyclocross, etc.
26"- mountain bikes, some urban bikes, down-hill mountain bikes, comfort bikes, cruisers, etc
29"- or 29er- bikes that use a 700c rim but take a much fatter "twenty-nine inch" tire. usually a cross-country mountain bike.

Read Sheldon Brown's article on Tire Sizing: https://sheldonbrown.com/tire-sizing.html

Tire sizing is confusing. What you're really looking for is the E.T.R.T.O. size of the tire, usually listed as something like 37-590. That would be a 37 mm wide tire with a 590 mm BSD.

As long as the BSD matches, you're fine. You can mix and match width of tires and rims to a certain point.

29'r refers to a mountain bike that runs over sized tyres on 700c rims which have a diameter of 622 mm and they draw their name from the wheel and tyres they use.

The 700c designation comes from the French and once denoted a 622mm road wheel that accepted a narrow tyre... there was once 700a, 700b, and 700d sizes but these are now obsolete and referred to medium, wide, and wider rims that accepted wider tyres.

The 26 inch tyre designation is probably the most confusing as there are many wheels / tyres labelled as 26 by X although the most common is the 559mm wheel/tyre that is used on modern mountain bikes that will come labelled 26 by x where x is a decimal.

Sheldon's article on wheel sizing pretty much covers it all and the system of using the ISO / BSD is by far the best way to confirm that a given tyre will fit a given rim.

and to confuse things further, a tire with a size designated by a decimal, such as 26x1.75, is not the same thing as a fractional size, like 26x1 3/4. again, the actual rim size ISO is what matters.

E.T.R.T.O. iSO standard, is a better disambiguation, as it is a agreement of the rim and tire makers
to use a common way to measure their interface, it's the Bead Seat Diameter .
inside edge of tires , outside of the rim where the tire bead hooks into the rim's groove
made for the purpose, in the rim extrusion.

And to totally confuse you, sometimes you'll encounter 69er and 96er. Mtbs that have a 26" wheel and a 29" wheel mounted at the same time, though I forget which combination is called 69er and which is 96er...

The numbers refer to wheel size and the corresponding tire. To lump each into a type of bike isn't accurate or helpful. I have 26 inch rims on my touring bike, which is a road bike. Or can I not ride it long distance and have to relegate it to an urban setting?