What is the difference between 26 and a 700mm bicycle?

Answer 1

26 is really 26 inch, a reference to the wheel size. 26" is a rather confusing size, with at least 4 non-compatible wheel sizes lurking behind the same denomination. You're better off using the ETRTO value, where 559 mm is the same as the most common/modern version of the 26" category.

700 is an old French sizing system originally based on the size of the inflated tire. It worked OK as long as there was only one tire width available, but failed miserably when manufacturers introduce tires of different width. It needs the company of a letter to become unambiguous.

Today, most common road bike size is 700C, which in ETRTO means 622 mm

So the short answer is that a 26" tire has a Bead Seat Diameter of 559 mm while a 700C tire has Bead Seat Diameter of 622 mm.