You might be thinking of temperature ratings, which are indeed just based on more stringent testing.
Radiation hardening is, well, harder. It typically means some combination of different semiconductor processes (often silicon-on-sapphire and/or larger feature sizes) and added internal redundancy (ECC memory, TMR, watchdogs, etc). All of these require that the rad-hard parts be manufactured separately from the commercial ones; some require that the part be designed separately as well.
Both cases occur in industry. The parts that only go through additional testing (radiation lot acceptance testing aka RLAT) are commonly sold as “radiation tolerant”. Parts that undergo hardening via design/manufacturing changes are often branded “radiation hardened”. In either case though, the available part portfolio is much smaller than commercial. Further increasing cost is that these parts are often geared for military/aerospace so have expanded temperature ranges, stricter qc, weird package types, etc.
it definitely wasn't temperature ratings, and it definitely was chips going into satellites. This was part of an internship at a place (I was in the "normal IC chip" testing zone, though).
I just might not be sure on the "space-rated" things being "radiation-hardened" or if it's more just "well they're gonna be more tested".
You're thinking about taking commercial parts and screening them for radiation tolerance rather than building parts from the ground up to be radiation hardened. Sometimes a vendor gets lucky and the chip has a pretty decent radiation tolerance that makes it useful for short duration missions. It's not going to last 15 years in GEO orbit but it could do well on a satellite only designed to last a couple years. It's not cheap to do radiation tolerance screening but it's way more expensive to make small batches of radiation hardened parts.
Sometimes the vendor will add a little more to the substrate that doesn't increase cost much but does provide a little bit more radiation tolerance. Other times there are certain things the customer must do like constantly rewriting registers. It's not perfect but you can save a lot of money taking an off the shelf TI part and flying it versus spending tens of thousands for something of similar performance but with a guaranteed level of radiation hardness beyond what you actually need. I've used a commercial TI ADC that works really well in a radiation environment (perhaps as long as 5 years in GEO) despite not being sold as such. We just decided to screen it to see how well it performed and based on that test data, we made the decision to fly it. I'm not sure who's idea it was but something about the design of the chip led us to believe it might perform decently. TI was not involved and was at first a little concerned when we told our sales rep we were planning to fly it.
Older chip designs use larger features that generally perform better in a radiation environment than newer designs using smaller features. An old 74-series logic chip might actually perform just fine when it comes to heavy ions but may not live as long as something like a 54-series that has a larger substrate that can absorb more gamma over time.
Another method is flying unscreened radiation hardened parts, they were built to a certain standard but you buy them without all the extra testing to save a few grand because you trust the vendor has a good process.
Radiation hardening is, well, harder. It typically means some combination of different semiconductor processes (often silicon-on-sapphire and/or larger feature sizes) and added internal redundancy (ECC memory, TMR, watchdogs, etc). All of these require that the rad-hard parts be manufactured separately from the commercial ones; some require that the part be designed separately as well.