It will say 38 Special +P on the barrel. The gun is not a "Detective" either as I don't think Smith ever used that term. If it has a hammer it is a Chiefs Special. If the hammer has a shroud it is a Bodyguard. If it has an interneral hammer it is an Centennial.
If it doesn't say 38 Special +P on the barrel I would be leary of shooting +P ammo in the gun even in small amounts. Federal, Remington, and Winchester all have 110 grain JHP's at standard pressure for such guns. Problem is the 110 grain bullet will probably shoot low as the odds are the gun was sighted in with 158 grain bullets. If the 110 JHP's shoot low try a 158 grain standard SWC (HP, if you can find it) or a 148 grain wadcutter bullet.
Some will advocate carrying the gun with +P and doing all your practice with standard ammo and that is one thing to consider. I have never been comfortable with that.
If you haven't been practicing with your Chief I would suggest limiting practice session to 20-25 rounds. I start off with a cylinder full of +P and do the rest of the session with standard ammo. I reload, but if you don't the 100 pak of Winchester sold at Wal Mart is good practice ammo. The cylinder latch will likely abrade your thumb so either wear shooting gloves or use a bandaid with the wound pad facing the cylinder latch BEFORE you start shooting.
If you are an experienced J frame shooter please forgive the above since I couldn't tell from your original post.
One last thought, there is no bullet that will make any handgun a hammer of Thor. I don't get hung up on one bullet as being the perfect bullet for self defense. I will load my guns with Golden Saber, Gold Dot, Hydra Shok, Silvertip, etc. I don't pay attention to internet reports about bullets where some guy shot wet newspapers or water jugs as I judge the chance of my being attacked by an alien water jug as pretty low. Choose any of the premium SD loads avaialble and you haven't "gone wrong".