A traditional twist-on radiator cap is always a "pressure" cap. Some of the modern screw-on types are not, but anything on an older radiator will be.
If by pressure, you meant a Lev-r-Vent type with the little red handle, that wasn't stock original either, but has been used by many people (including me) because they're so handy for releasing pressure.
Your new one that came with the radiator likely has a higher pressure rating though. Stock was what, maybe 13lbs? ? And the new one is maybe 16lbs? That would be the most obvious difference, including the looks/colors/shapes between that and another manufacturer's product.
Do you run a recovery tank? Or is the radiator vented to ground?
Likely your old one will still fit (not guaranteed, but very likely) and you can probably use either one. Higher pressure raises the temperature before it spits out or boils over, but does not offer any improvement in actual cooling from that aspect.
However, more pressure inside the system can help with hot spots and improve efficiency if there is already an issue revolving around that kind of problem.
Not as effective perhaps as higher water pressure from a high-flow pump, but still an improvement. Just have to hope that all of your other stuff is up to that increase in pressure.
Paul