F-150 Tow Package vs. Trailer Prep

I am looking to buy a 2005 F-150. The dealer says that the truck has the tow package. As far as I know, the prep package is just the wiring harness and hitch and the actual tow package is the additional oil coolers and the transmission cooler. Am I correct in that assumption? Also, the dealer says that the truck has the tow package. Is there a way that I can verify that by looking at the truck itself?

Thanks.

Look for the cooler in front of the radiator.

Tow package should also include a heavy duty hitch assembly, the whole hitch assembly should either be welded or bolted directly to the bottom of the frame and not just a hitch ball bolted to the bumper.

Having a shift kit installed in the tranny would not hurt either if it has not been done already, my 77 F-250 has a stage-2 shift kit that made it shift really quickly which reduces heat and friction inside the tranny.

The cooler on mine was kind of a two stage system, the tranny cooler line/lines left the tranny then went through the cooler ports on the bottom of the radiator then went to the tranny cooler in front of the radiator then went back to the tranny.