They make ALL of the above ! I use a double burner version in my leaky, uninsulated garage hours at a time in winter.
They do, but catalytic burners burn pretty complete when they're hot. When all you see is a glowing screen and nothing else, it's not making significant amounts of CO. That's because the combustion is so complete, that no carbon chains are getting out.
If you put your hand over a venturi hole while it was burning well, you can see a faint greenish flame start to appear over the screen. The visibly incandescent exhaust is a sign of incomplete combustion, and CO being produced when it runs rich.
FWIW, I had a single burner one of these, and while I really liked what it did, I found that a quartz electric heater cost me less in the long run (because of the exorbitant costs of refilling my BBQ tanks here), so I ended up selling it.