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For instance, in some cases I will see a particular bike tire listed as available in 700x25, 700x25c, 700c x 25, and 700 x 25mm. (Just picking out a number here, it could be 23, 25, 27, etc.)

What, if any, is the difference between these? I would think that 700x25 is the same as 700 x 25mm, but I'm not so sure about the "c" when it lists both "700x25" and "700x25c" as sizes for the same tire on the same site, and lists different prices for each!

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It doesn't mean anything, really. It's a historical relic.

At one point in time, "700c" was a standard tire/rim size, where "c" indicated the bead seat diameter and "700" was the diameter, in millimeters, when the tire was installed and inflated.

That "700c" tire size has a 622 millimeter bead seat diameter. There's an ISO standard that's often listed in small print where those tires are all '25-622'. This is the same as "29er", though usually tires marketed that way are substantially wider. "700", "622" and "29" are really all the same size.

All those tire sizes you list are the same. If there were different prices for the "700x25" and the "700x25c", it's because there was some other difference between the tires, like model, threads per inch, bead type (wire or kevlar), etc...

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    The other widths were designated 700a, 700b, 700c... you get the picture. Each tire/rim combo resulted in the same total diameter (three different rim diameters and three corresponding tire widths.) 650 sizes were similarly specified as 650a, 650b, 650c...but 650b (iso 584 mm) was the one that stuck.
    – WTHarper
    Commented Jun 12, 2013 at 3:55
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    More at sheldonbrown.com/tire-sizing.html#french
    – armb
    Commented Jun 12, 2013 at 11:39
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    The letter was the way that the French system of tire/wheel sizing specified what we now call bead seat diameter (BSD). In the French system all '700' wheels were supposed to have similar ODs (close to 700 mm). Different rim sizes made it possible to go from a skinny racing tire to a wide touring tire. A relatively wide tire (32 mm or so) would go on a 'C' rim which had a BSD of 622 mm. The system was designed to facilitate changing tire width while keeping the OD constant. The problem was that then you had to adjust brake height as you switched rim sizes, so it wasn't all that convenient.
    – dlu
    Commented Jul 18, 2015 at 14:03

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