Depends on the year. Sometimes FX4 is just some accessories, other times FX4 is a trim level between XLT and Lariat.

4 x 4 just means that it is a 4WD.

4x4 Offroad is an earlier version of FX4.

For the most part, 4x4 Offroad and FX4 gets you skid plates under the transfer case and fuel tank, all-terrain tires, limited slip diff, shocks that say Rancho but really aren't, and a decal on the rear quarter flank.

For years where FX4 is a trim level ('08 and up IIRC), it gets you all the equipment of an XLT, plus the accessories I mentioned above, and maybe a few of the Lariat trim stuff, plus painted grille and mirror covers.

Other than being a 4WD, none of these things make any changes to the drivetrain, frame, body, etc. Same basic truck.

It is also interesting to note that F150 equipment for the various trim levels is totally different than the Superduty line. Even though they use the same names, the similarity stops there.