Right,
I will elaborate on the part numbers. Or at least the information I have read confirms this (mainly Rennlist)
951 106 031 02 (I think it was this) is the part number for the first batch of 951s (I.e the 220 Turbos). This by Porsche was superseded by the rad ending in 50.
951 106 031 03 is indeed the S2 rad. Whether or not you can still get the rad down to this number is another question, despite some new rads being advertised with it.
951 106 031 50 is the 250 Turbo Rad. It seems to have a similar core to the S2 rad (probably the 220 too) but the tanks are a little larger on it.
When I got my rad, it was a 50 variant rad, and it fits fine. Some think this has superseded all previous 951 rads (It wouldn't surprise me considering it would be cheaper to do from an economies of scale perspective).
FWIW, Euro Car Parts is the cheapest place for a new LRO branded rad (I.E what the Porsche rad is). It even has Porsche scribbled off blatently where it was on the old rad!. I paid 240 for my rad (now around 260 due to VAT changes) although I did haggle a little. Berlyn wanted 330, Porsche were a similar price as were JMG. Porscheshop came close at 280, but ECP were pretty quick in getting it in and for me anyway the service was good.
Mine was not as bad as yours but I still noticed the benefits. Main ones included the fan staying on for less long (30 seconds vs. a couple of minutes (Something EMC noted me about 944s), and the temperature was more consistant (I used to see the car's temp rise up before as soon as I hit a traffic jam...).
Whilst you are there, it may be worth changing the heater and cooling hoses too, which will also help cool your car down better if they are swollen etc. (likely if they are the original items). The cheapest place for these was Berlyn, with him being quite helpful. I bought a top hose, bottom hose, heater elbow hose (these all seem to swell up) and a genuine Porsche thermostat (seemed better built than the cheap GSF thing I put in). The Stat cost me 14, with the pipes coming to around 46 all in.
Here's the difference between an original S2 '03' rad and a '50' 250 Turbo rad:
Top of the old rad has been cleaned for clarity. The question is, would you have said that rad was shot?


I wonder what was written here...

Another thing. Only use non OAT Coolant in the Porsche cooling system that is Phosphate free (a BS marking of BS6580 will confirm the latter). Unipart CoolBlue will be fine as will Comma's Glytasyn G48 (Which Common solely recommend for the 944). Whilst some may say OAT will be fine (I.e Red/long life coolant) and it will indeed potentially bring benefits to other parts, the 944's matrix is made of good old fashioned Brass and Copper, not great with OAT coolants.