The difference is that in 1958, S&W stamped "MOD 37" on the yoke. The .38 Chiefs Special Airweight that left the factory 5 minutes earlier did not have MOD 37 on the yoke. Same gun.
Prior to 1958, ALL S&W revolvers were referenced by a name. Such as "Chiefs Special", "K-38 Masterpiece", "K-38 Combat Masterpiece", "K-22 Masterpiece", etc. Beginning in 1958, all S&W revolvers received new designations, that being "Model nn". Such as "Model 36", "Model 14", "Model 15", "Model 17", etc. Each of the new Model designations were then stamped on the yoke as "MOD nn" where nn was a number.
As significant engineering enhancements were made to each model revolver, the model designation went to a -n, such as 14-1, 14-2, 14-3 etc. And they were so stamped on the yoke as "MOD 14-1" and on down the line. So, again, technically speaking, if MOD 14 is not stamped on the yoke, the gun is not a Model 14.
If your airweight was made in 1955, and a stamped Model 37 was made in 1958, there is not an iota of difference in the quality of the gun. That is my opinion, since you asked.
Enjoy your Airweight. That is one that is still on my list.