I started typing out a rather (what I considered to be) lengthy explanation , but decided to see if I could find a more succinct answer online. Found this in an old thread discussing just this subject over on the Colt Forum penned by a member known as "1903joe"; not shorter but explains it pretty well and probably better than I could have, so . . . .
"Yes, the 32 and 380 auto springs are interchangeable.
There are different appearances in the springs over the years the 1903 was produced, as they were originally shipped from the factory, but I'm not sure if the differences are aligned with the generally recognized distinctions made by the five "Types" collectors recognize. (I know Brunner has some discussion of springs in his book; I think he discusses the numbers of coils in different recoil-springs from different time periods, but I'd have to look at the book again to refresh my memory on exactly what he says.)
Generally, with a straight blow-back pistol, like the 1903, one has significant flexibility with recoil-spring strength. The spring can be more properly described as a "slide return spring" than a "recoil" spring. It is the friction from the expanding cartridge case (exerted against the chamber walls), caused by the extreme pressures generated from the burning powder, which is keeping the barrel as a "closed tube" when the gun is fired. Only after the bullet has left the barrel, and chamber pressure starts to drop, does the spent shell casing really start to move and begin its push against the mass of the slide and resistance of the spring to start the process of cycling the action.
If the recoil-spring is too strong, the slide will not move with enough velocity for proper extraction of the spent shell casing (it's a "flicking" motion between the extractor and the ejector). If the spring was so extremely strong, it might not even move the slide all the way to the rear so the next round could be stripped from the magazine.
If the recoil-spring is too weak, the slide will move with such velocity, it will stress the gun as it reaches its maximum rear-point and stops with a "pounding" to the frame. An extremely weak spring may not have enough strength to strip the next round from the magazine and chamber it properly.
Between the two extremes of very weak to very strong, there is a lot of flexibility with recoil-spring "weight." One of the best ways to determine if the recoil-spring strength is proper for a particular pistol is to evaluate how the spent shell casings are extracted. With a strong shooter firing it (no limp-wristing) simply watch how far the spent shell casings are tossed. If they are hardly tossed any distance, but more-or-less tumble to the ground, the spring may be too strong; if they're tossed out 20 feet away from the shooter, it may be too weak.
If the spent shell casings are being thrown 5-10 feet away from the shooter, the gun is feeding and extracting reliably, and the spring looks to be in good condition (no kinks, bends, rust-pits, etc. in it) I wouldn't worry about what the specific "weight" for it is."
This explains it pretty well, though I'm sure some could chime in with a different opinion, though it would have to be backed but by hard data before I would change my opinion on the subject. What seems 'right' to us sometimes goes against we feel does or doesn't make sense. The physics, engineering, and design for the reliable operation of semi-auto and full auto actions is a study unto itself and the less successful attempts often hinge on a razor's edge of applying the math to practical application.
