It's not just Teflon that off-gases and kills birds. It's any coating that contains any of the "Fluorinated Compounds", such as PFOA, PTFE, etc., and there are a ton of them. "Teflon" is actually a brand-name of one particular coating that contains one or more of these Fluorinated Compounds, but is not actually a chemical or compound itself (Teflon is kind of like "Kleenex", it's a brand-name of facial-tissue, but we tend to call ALL facial-tissue "Kleenex"; Teflon is the same way, we see a black-colored non-stick coating on a pot/pan and say it's coated in "Teflon", but that isn't the case at all unless it's made by a company who is licensed to use Teflon specifically). So a lot of the time people think that if they call-up a manufacturer and ask them if a product contains any "Teflon" and they say no, that means it's okay to use around birds. And that is what typically gets people in a lot of trouble.
Typically any pot/pan that has a black-colored non-stick coating on it contains some Fluorinated Compounds and is unsafe. Just the same as some griddles and hot-plates, such as the George Foreman Grills, which are very unsafe and contain all kinds of Fluorinated Compounds in their coating. So you should always call the manufacturer of a product such as pots, pans, grills, griddles, hot-plates, space heaters, blow dryers, etc.
As far as pots and pans go, the Ceramic non-stick ones are fine, Stainless Steel is fine, Cast Iron is fine, and the REAL Copper ones are fine, meaning the expensive ones that are ALL Copper, not "Copper-plated", as a lot of those contain Fluorinated Compounds throughout their make-up under the Copper-plating.