Sorry Alan, but the description I gave above is quite correct (though lacking some detail). I'm afraid you have got completely the wrong end of the stick here.
The difference you are observing between two different "500mm" lenses, assuming that you are measuring then both under the same conditions and focused on infinity, has nothing to do with maximum magnification, it's a simple difference in actual
focal length as opposed to nominal
focal length. It rather annoys me (and probably you too), but it's a fact of life that lens makers often crib a bit with their claimed focal lengths, and always (it seems) to their own advantage.
Maximum magnification, also known as "reproduction ratio" or just "magnification", is a standard performance metric used by lens designers and makers, and routinely quoted in their technical literature. Indeed, those examples I gave above were from Canon specification sheets. As examples of others from the various lens makers, you may care to look at some official Sigma specifications here
and discover that the Sigma 17-70 has a maximum magnification of 1:2.3. Or go here
to discover that the maximum magnification of the Nikkor 400/2.8 is 1:6.3, here
to see that Pentax cite the maximum magnification of their smc FA 31/1.8 Limited as 0.16 (which you can divide into one to yield 1:6.25 if you prefer to see the number as a ratio rather than a fraction), or indeed here
to discover that Tokina cite the maximum magnification of their 80-400/4.5-5.6 as 1:5.4.
Maximum magnification is measured at the minimum focus distance. Does it seem odd that the lens makers cite that figure when anyone smart enough to count change could divide the focal length by the MFD to discover it for themselves? There is a reason: focal length is always measured with the lens focused at infinity, while (obviously) maximum magnification is measured with the lens focused as close as it will go - and this changes the focal length! (Lenses are shorter when focused for close-up. You can easily see this for yourself by spending a few minutes with a macro lens and turning the manual focus ring.)
By knowing the focal length and the MFD, you can approximate
the maximum magnification, but to get it exactly you then need to allow for the change in effective focal length at close focus. (I imagine that's a fairly small correction with most lenses, though I've never troubled to do the maths for myself.) In reality, there is no need to: I can see at a glance that the 100-400 has a much higher maximum magnification than the 500/4, or if in doubt I could look up the factory specs to discover that the 500/4 has a maximum magnification of 1:1.2 where the 100-400 is nearly double at 1:2.