The Terrier was originally built on the I-Frame but later models were built on the J-Frame after S&W discontinued the I-Frame.
FWIW the -1 model number nominally indicates that the OP's friend's gun is a J frame. An I frame gun should not have the -1 suffix.
The M32 was normally offered with a 2" tapered barrel, a fixed rear sight, and a round-butt grip, i.e. without the sharper and straightened corner at the rear of the butt. IIRC blued and nickel finish were offered but nickel is uncommon. Guns built before the mid-60s normally had the so-called "flat" (non-scalloped) cylinder latch, and pre-1968 guns will have diamond-shaped escutcheons around the grip screws; examples with these features carry slightly higher value. Other than the finish and the grip and cylinder latch changes, I am not aware of any other options or unusual M32 variants, although this is subject to a mandatory disclaimer: the only hard-and-fast rule about old S&W's is that there are few hard-and-fast rules.
FWIW the Model 33 ".38 Regulation Police" was similar to the Terrier, but was normally built with a 4" barrel and a square-butt frame. IIRC both guns were discontinued in the mid to late 1970s.
While it is unlikely to even chamber, it is unsafe to attempt to fire a .38 Special cartridge in a revolver chambered for .38 S&W due to the difference in pressure.
FWIW every J frame M32 (and M33) I've ever examined had a physically shorter cylinder and correspondingly wider front cylinder-to-frame gap than a contemporary .38Spl J frame. They also had shoulders in the chambers that appeared to be cut at the correct depth for a .38 S&W case, which will cause a .38Spl case to project from the cylinder by ~1/4", rendering it impossible to close.
Also, one word of caution...
...Fiocchi offers a FMJ loading...
Past information on the S&W forum indicates that some later .38S&W J frames were built with 0.357"-caliber rather than 0.361"-caliber barrels*, thereby allowing the .38S&W and .38Spl guns to use the same barrels, which simplified parts inventories. However, there is some concern that firing a 0.361"-caliber FMJ bullet through a 0.357"-caliber barrel at low .38S&W pressures may result in squibs- i.e. stuck bullets- which can damage the barrel, particularly if follow-up shots collide with the first stuck bullet.
Until you can verify the barrel size, I would recommend using lead bullets rather than FMJ; OTOH there is little concern that the typically very soft lead used for .38S&W bullets will cause squibs. (Yes, firing oversize bullets will typically cause pressure spikes, but this is generally inconsequential when using a very low-pressure cartridge in conjunction with a relatively strong modern revolver.)
*Mandatory disclaimer: I have NOT been able to independently verify this information.