Is plus p the same as special when refering to ammunition?

No. Nein, Nyet. Just in case you missed it, NO.

+P is a way of denoting cartridges which are loaded to a higher gas-pressure than what is considered normal for that cartridge.

For all intents and purposes 'Special' should just be held as a name. In some cases when a manufacturer would bring out a new cartridge firing a bullet diameter shared by another cartridge they would call it a 'Special' to distinguish it, but that is a much longer discussion to cite the various and sometimes contradicting methods in which the term is applied.

In the case of something like a .38 Special; the +P version would be .38 Special +P; indicating a higher-pressure loading of the .38 Special cartridge.

Not all guns are created equal and while most modern-production guns can safely use +P ammo (at the cost of increased wear on the gun) this is not a universal rule; and you should never use +P ammo in a gun if there is any question of whether or not it can handle the higher pressures.