I applied for a USA C1 transit visa. My visa was approved, and when I received my passport, I saw that the visa class is B1/B2. Did I get a regular visit visa or am I missing something?
Yes, you got a regular visitor's visa. You can also use that visa for transit, so the visa officer basically did you a favor, allowing you to visit the US in the future without having to pay an additional visa application fee.
A B1/B2 visa is indeed a regular tourist/business visitor visa. It is also good for transiting the US.