According to the brochures of the relevant model years and to the TruckPlanet website, the 1960-81 Chevrolet COE "Tilt Cab" trucks were sold just as "Tilt Cab" models from 1960 to 1972⁽¹⁾. With the Titan 90 (unveiled in 1968) known as "Aluminium Tilt Cab", the "new" 1973 standard Tilt Cab became the "Steel Tilt Cab", even if the "Steel" was sometimes forgotten (see the 1979 brochure)...

For the record, the change between 1960-72 and 1973-81 trucks seems just to be a face-lift, targeted mainly on the grille:

1960-72 cab (with dual headlights only for the 1960-61 model years?)	1973-81 cab (without the "blinker mustache")

So, for purposes of accuracy, as the first name given to this truck was just "Tilt Cab", and as it was longer sold with that name, shouldn't we identify at least the 1960-1972 models just with this shortest version?

About the GMC version: as GMC already had an "Aluminium Tilt-Cab" since 1959 (the 1959-68 F-Series / F-Model⁽²⁾, aka the Crackerbox), and as far as I have seen, the twin of Chevrolet Tilt Cab was named from the outset "Steel Tilt Cab", "Steel Tilts", "Steel Tilt models" or "L-Series" in brochures, "Steel Tilt Cab" being apparently the most common.
Maybe we should put the two 72" Steel Tilt trucks⁽³⁾, the single L-4000 model and the lonely L-Model one with their 39 "Steel Tilt Cab" pals?
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(1) 1961, 1966 and 1972 brochure
(2) Once again, a slight gap between official name and "common use". For now, the only GMC reference I found about F-Something Cab-Over-Engine trucks is "F series", and apparently only enthusiasts sites talk about "F-model", of course without any reference
(3) 72" / 1.83 m was the BBC (Bumper to the Back of Cab) length of the standard cab.

Done
The GMC are listed as "Steel Tilt Cab" and the Chevrolet as "Steel-Tilt Cab".
Is that correct or should both have the same name?
(I suppose we could remove the "-")

For what I have seen, there was no hyphen. When you say "done", you mean for the GMC only (thanks for it, by the way), or will all Chevrolet keep the "Steel Tilt Cab" name?
I'll check the pictures to (try to) give a generic (1960 or 1973) model year for the 16 non dated trucks.
I still don't know if the dual headlights grille changed at the same time as the C/K-Series (1962), but I keep on searching

I said done for the few links you gave, I missed the fact that "steel" had to be removed from the name of the Chevrolet.
So I can change all "Chevrolet Steel-Tilt Cab" to "Chevrolet Tilt Cab" ?

That's a good question... 1973-81 models were called Steel Tilt Cab.

If the "Non-steel" / "Steel" idea is kept, then you can rename these 5 1960-72 models as Chevrolet Tilt Cab. (I hope someone said in a comment why the 1964 MY was given... For now, I didn't find any clue about year to year changes.)
For the 16 not dated trucks, I'll give in each page. a generic model year (and a "Non-Steel" / Steel" indication) as soon as possible

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...)