That may be true for the Federal ammo you have, but as above, .38 +P+ ammo was custom made for the department or agency that ordered it.
Since there is no SAMMI standard for it, it was custom made to whatever power level the customer wanted.
Some wanted more powerful ammo that could be used in standard .38 Special revolvers, which is what it sounds like you have, some ordered it loaded to near-Magnum levels for use only in Magnum revolvers.
The point is, you have to be careful with +P+ ammo because unless it's in a box with load details printed on it, you have no idea what you have.
You could have some ammo made to be fired in ordinary small frame .38 Special revolvers, or loaded hot for Magnum revolvers.
Make a mistake and you could blow a gun.
For what this looks like, check out the Kuhnhausen Colt Shop Manual pages 47, 48, 49, 127, and 128 for pictures of Colt "D" frame guns blown apart by +P+ ammo.