I can't find any information that says that Winchester changed choke tube specifications at any point during manufacture of the 1200, 1300, 1400, 1500, & Ranger shotguns.
The 120 is an economy-grade 1300 with a hardwood stock, which means that it was manufactured with the Winchoke system.
Carlson's says that the following tubes will also work in the Winchester models I listed above:
"Interchanges with Carlson's Winchester, Browning Invector & Mossberg 500 style threads"
Briley says the same thing as Carlson's, as does Trulock.
Frankly, for the prices they're asking for "1st style" and "2nd Style" Winchoke tubes I'd take your barrel to your local gunshop and see if they have any of the tubes I've listed above (just to make sure that they fit properly) and buy from your local shop or from Midway or Graf and Sons.