W.B.lbl has now commented to me that both variants are Bridgeport pressings, but the copy with the really deep groove would be a later pressing. He also says that the labels would have been 3.875" in diameter originally, but shrinkage occurred while pressing.
Since both variants bear AW labels, that would mean that the deep grove was introduced in late January 1920.
This 1920 Columbia release from 1920 comes in two versions, with and without large pressing ring. The pressing ring is 2mm = 0.0787402 inches wide and has an inner diameter of 7.5cm = 2.95276 inches and outer diameter of 7.9cm = 3.11024 inches. The label itself has a diameter of 9.8cm = 3.85827 inches.
Please don't ask me how many 16th of an inch any of that is. ;-)
Anyway, I wonder if this is a sign of different pressing plants and if they can be identified.
The fonts, now that I look at the variants again, don't actually seem to be different.
"Slim Trombone' was one of a suite of trombone pieces wrritten by Filmore. Each part of the suite was supposed to represent a different "character". Probably the most well-known part of the suite is the one known as "Lassus Trombone".
Also good to move them up if mine are slightly older. Following numbers are stamped on labels: Side A: '109' and '2', also 'CA. S' / Side B:'139' and '3', also 'D-BA'.
Actually, the fonts on both of your sides are different from the ones on mine although they seem to be of a similar design and time period otherwise. My labels could be slightly later than yours because they had updated price stickers attached at some point that an earlier owner then ripped off. Yours also have the take and stamper numbers embossed under the label. If you can read them, we could add this info above.
Since the gold on your labels is less faded, I moved yours to the front.