Done! And thanks to Ddey65 and to some searches, I can now refine the identification:

The side emblem seems also to be a clue for better identification, but for me it's still a work in progress. And apparently early models were Viking (T-60) or Spartan (T-70 and T-80) trucks, but I think it was no longer true for the 1962-63 models, as for the C/K- and L-Series. Anyway, as the model number is most of the time (always?) invisible, there is usually no clue to tell the difference between a T-60 and a T-80...

As far as I understood, the T-Series line:
• started in 1960 with T-60, T-70 and T-80 models, all sharing 4 wheelbases from 97" (2.46 m) to 145" (3.68 m),
• lost (for some years) the T-70 in 1962, but proposed a Diesel engine for the T-80;
• gained a T-50 in 1965 together with a possible 5th wheelbase (175" / 4.44 m) and Diesel engines for the whole trucks line,
• and introduced a TS/TE-40 in 1967 when the line got a 2 letters + 2 digits name nomenclature (TS/TE for 40 to 60, TM for 70 and 80).
As for all other trucks lines, heavy-duty trucks with a tandem rear axle were given a "M" as letter (M-80: 1960-66) or later a "W" as first letter (WM-80). And of course these codes change when the truck has a Diesel engine...

I found less documents for the "2nd generation", but apparently:
• the line included only TV-70, TM-80 and TW-90 trucks at first (WV-70, WM-80 and WW-90 as tandem),
• then new change in 1975 with only TE-60 and TE-65 series, both available with 133" (3.38 m) or 175" (4.44 m) wheelbase
• and just for the fun, in 1979 TE-60 was changed to W-60, and TE-65 to W-70.

In short, the usual mess of Chevrolet, so let's just call them Tilt Cab and Steel Tilt Cab
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(Next episode: the GMC models. Stay tuned...)