What kind of wok do I have?
Types of woks:


Stainless Steel


Heavy, expensive and well, shiny like stainless steel. Unlikely that this is it.

Cast Iron


They're usually pretty heavy. It'll be black, but due to your weight, I'd guess that this isn't it either. Lightweight cast iron woks exist but they can be pretty brittle.

Carbon Steel


Lightweight and cheap. Will be black if it's seasoned/pre-seasoned. These are manufactured a number of ways (hammered, stamped or spun on a lathe). Depending on what you mean by "swirls", it could be a result of the manufacturing method, the "bad paint job", could be the some pre-seasoning (ie: bad seasoning job?)?
This would be my guess as you said it's lightweight and cheap. The Chinese lettering would also make it more likely as this is one of the more popular traditional types.

Teflon, Aluminum, other...


You can also find them in various other materials, but these should be pretty obvious, and you're unlikely to buy one randomly I would guess.



TLDR: I would guess it's machined/turned carbon steel.



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