I believe it's different for the 6 cylinder versus V8 so that will affect responses obviously. There are several older posts on this forum about changing the cats and in the case of the V8 the stock configuration has three catalytic converters - one for each cylinder bank and then after the last cat the exhaust becomes a single pipe and goes into a muffler before the tailpipe. There are complete cat assembly parts sold having all three pre-welded that I believe require you to loosen or remove a crossmember on underside of frame to fit. But I've heard other guys buying separate universal fit components piece it together as well. I usually try to tackle DIY stuff on the Explorer but this is one job I left to my local shop.
Rob is right. My V-6 has two cats, one for each bank of cylinders, the outlets from which merge by means of a cross-pipe, which then passes ABOVE the crossmember and enters a big muffler. Getting the 2 cats and their outlet pipe out of the vehicle is quite a hassle. I expect muffler shops cut them out. With 160k on them now, the nuts holding the muffler flange and exhaust pipe flange together, have no visible "flats" left. I will have to cut the bolts, very tight work space. Replacement of both cats may be done as Rob says, piecemeal, or one piece.
V-8 I have heard uses a third cat, where my Ex has a plain muffler. I cannot confirm that, though. imp