I have two examples of 820LR (Sporrong and Gumaelius reverses) and both measure 22.4 mm. However, this token is not round (see attached) and there are at least two reasonably logical ways of measuring it. You can take point to point (blue on my example), essentially treating it as a circle with bites taken out of it, or you can interpret it as a square with bites taken out, where the original edges are marked in black on my example and the measurement is in red. My 22.4 mm is the blue measurement I think; I'm not at home to check so only have access to digital records.
820MM I don't have so I can't shed any light there. Can you post a picture? I can then see if it's written up elsewhere (e.g. Stockholmspolletter).
More generally I often find that the diameters given in Smith aren't that accurate. I don't know whether this is because he didn't use a caliper and preferred to align the token with a ruler, which is always going to be less accurate, or whether he originally measured in inches (quite likely given someone in the US in the 1960s) and converted to millimetres with an inaccurate conversion factor or dodgy mental arithmetic. Or both. Usually I ignore the diameters given where the diameter is not the only distinguishing feature between two or more varieties, and where it is the only distinguishing feature, I just note that Smith has "bigger" and "smaller" variants. I then measure them for myself according to whatever accuracy and criteria suit me.