My great grandmother died recently, and among the things left to me were a few of the guns that had belonged to my great grandfather who died several years back.

I have had very little handgun experience, so I'm not clear on a few things.  Could you guys help?

The barrel is stamped 38 S&W SPL.  What is the differnece between a 38 S&W, 38 SPL, and 38 S&W SPL?

Also, can anyone suggest a way to identify what model it might be so I can read more about it?

What is the differnece between a 38 S&W, 38 SPL, and 38 S&W SPL?

.38 Special and .38 S&W Special are the same thing. The .38 S&W is an older caliber of lesser power and different dimension than the .38 Special. Most likely you have a S&W M&P (Military and Police) revolver, known today as the Model 10.

After looking the weapon over one more time, I noticed that in the yoke was stamped MOD 36, so I assume that it is a model 36.  I noticed Winchester 38 SPL +P ammunition was on clearance at a local shop.  Do you think this little gun can handle the +P?

If it's a Model 36, it may since it's of later production. I would call S&W and ask to be sure.

Ah, the mod 36. The Chief's Special. You've got yourself a great little gun. Whether or not it can handle +p is entirely dependent on the date of manufacture. Check the smith and wesson website www.smith-wesson.com or call them to confirm

FWIW, the outfit I used to work for put +P ammo through model 36’s continually for years with no major problems.  However, after a while (maybe a thousand rounds – wild guess!) they would start getting out of time.

Yes, some Model 36's are rated for +P while others are not. But let me say this....either way it should be capable of firing the cylinders 5 shots using +P without any problems. Just don't shoot this stuff all of the time and keep it only for times when your life may depend on having it. BTW, one of the best loads out there for this gun is the old 158 gr +P lead HP's, often referred to as FBI loads. These seem to perform well from these short barrels and is Massad Ayoob's top pick for this caliber and particular pistol. Evidently the total lead bullet expands better at lower velocities than those using a copper jacket. Interestingly enough, some of those top ballistics people such as Fackler and Marshall rate this load as near equal in stopping performance as the .45 ACP hardball. Not bad.