I currently have a 2001 4x2 extended cab. The frame is bad. I've found a frame from a 1998 4x4. Are these the same frames?

 

Generally speaking, from 98 all the way to 11, the Ranger went very few cosmetic changes through those years. From 2004+, things started getting crazy in comparison to it's older model years, but in most situations, 98-03 are for the most part the same truck.

Of course there are some differences (not only cosmetically), but for your chase it shouldn't matter.

The difference between 4x4 and 4x2 is not only the capabilities, but the front axel and hubs, knuckle setups, the suspension is different (torsion bar for 4x4 and coil sprung for 2x4 except on edge models), the brakes on the front are different as well, and there's some electrical components that are different as well.

All in all, it's some work to do this, but there shouldn't be any need for fabrication. You should be able to swap all of your 4x2 01 parts over onto the 98 4x4 frame. Just make sure the frame you get is from an extended cab as well otherwise it won't be long enough for your cab and bed to bolt on.