Corolla/Prius catalytic converters: Interchangeable?

I have a 2008 Prius and fell victim to the catalytic converter thieves last night. The replacement is backordered for two weeks(!!!). I was looking at parts available at my local auto parts shop, and they have new certified catalytic converters for 2008 corollas that look, to me (nonmechanic), identical, and are ~$1,000 less expensive. I figure that even if the piping is slightly different (diameter, for instance), that could be adapted for <$1k and in <2 weeks. Since they're both Toyota it seems unlikely to me that they'd design two completely different catalytic converters that are the same shape, function, and model year.
Question: What differences might there be between a Toyota Prius vs Toyota Corolla catalytic converter that I'm not thinking of? Could I use a Corolla converter to replace my stolen Prius one?
P.S. I live in California where there is a strict smog regulation called CARB. It basically means you must buy a certified aka Toyota OEM part or you won't pass smog checks -- even if the car's exhaust is ok. So the options are very limited here.

Edit to add:
Toyota part number of what I need is:
Prius: 1741021500
Corolla: 1741022500 (close enough to above??)