For 1997, 2WD, 5-door, North American Ravs I get different part numbers:
Automatic: 16400-7A122 (RADIATOR ASSY)
Manual: 16400-7A111 (RADIATOR ASSY)
Most probably though, as Lugnut suggested, the only difference would be the extra outlets for the transmission cooler.
I though so. I saw that at the bottom of all the radiators "online" that I was looking at had water outlets piping. My radiator doesn't. So Toyota 16400-7A111 it is. It has a very small leak and for me, radiator stop leak just won't cut it. As you can see it has a minor leak.
Change or rebuild power steering pump.
Maybe rebuild the Rack and Pinion if needed.
Can you determine exactly where the leak is coming from? In the past when I have had a small leak I have been able to take the radiator to a radiator repair shop and they would repair the leak for much less money than a new radiator costs. But that was in the day of all-metal radiators. If that isn't possible then it may be possible to buy a rebuilt radiator, or even one from a car salvage yard with a guarantee that it won't leak.
I just took a quick look on RockAuto. ~$70 to $100 for a new radiator for mine. Yes, in the old days you'd get a brass radiator "boiled out", repaired, and repainted but not at these prices for plastic and aluminum.
I used the same radiator for the automatic in my 5 speed. I was debating running my transmission cooler lines through it and then link it to the transmission cooler. I don't know if it would gain much other than more fluid.
I don't know if you have completed this or not but here are some pointers.
Make sure you take the following off the old radiator:
1) sensor near the lower radiator hose output.
2) lower vibration pads
3) upper mounts
Inspect you cooling fans, mine were in bad shape, lots of corrosion. I replaced them with a pair of Upgr8 Universal High Performance 12V Slim Electric Cooling Radiator Fan With Fan Mounting Kit (14 Inch, Black) - Amazon.com. One big advantage is that you can easily slide the radiator into place with the fans mounted.
Unless you have replaced the thermostat, radiator cap, and hoses in the past year get new ones.
Inspect your heater hoses and all those outlet hoses that you can (two are under the exhaust manifold). There are also hoses going and coming to the throttle body and one last hose going to the back side of the heads running just above the fuel injectors.
Flush out everything until it comes out pretty clear particularly the heater core before you put your new stuff on.
But I'm sure you know all that, mostly for others that follow these threads.