All cats are not created equal. There are 2-way and 3-way cats and 3-way w/air cats, as well as 'main' catalytic converters, and 'pre' or 'light-off' catalytic converters. All are designed to perform a specific task. If you want to know which catalytic converter to use on which application, you have to determine the type of catalytic converter(s) originally put on the vehicle. This information (required by the EPA) was originally on the vehicle emission control information label somewhere under the hood - different locations on different cars - hood underside, shock tower, radiator support, fan shroud, firewall, etc. The labels will ID the cats with stuff like:
Two-Way (Oxidation) = OC or COC
Three-Way (Oxidation Reduction) = TWC or ORC
Three-Way + Air (3-Way Plus Oxidation) = TWC/OC or ORC/OC
In addition, replacement cats are also categorized according to vehicle weight and engine size.
THEORETICALLY - to pass an emissions test anywhere, you have to have either the same type/number of cats on the car that came on it originally, OR a single replacement set up designed to treat the exhaust stream in the same way the original multiple cats did, AND the set up has to pass the sniffer. I say theoretically because as a practical matter here's what really matters:
The guy or gal that inspects your car that day at that station (doesn't matter where - CA, or anyplace else) has to say OK. That's the only rule that matters. Doesn't matter what the state/local rules are, doesn't matter what the EPA said, doesn't matter what you think you know about the regs. What matters is will that inspector say yes to your car. That's why all this banter on the forums is helpful -- but limited in it's ability to help any particular person get their car past the test. Because if the person inspecting your car that day wants to see two cats on each side, and you've only got one - it don't matter that you think the rule says you can replace two with the correct single cat. Likewise, if the person just wants to see a cat, and see that you pass the sniffer - it don't matter that the rule says you've got to have the same number and type of cats that originally came on the car.
Bottom line - you can't generalize your particular inspection experience to someone else's car/trip to the inspection station.