Oh yeah, it must be in there. If you were to etch down to the chip with acid I’m sure you could see it.
Contactless has two forms. The old one is mag-stripe emulation. It would literally just respond with the information from the mag-stripes. It was exactly as secure as mag-stripe. Probably worse because you didn’t need to physically move the card over a read head.
That’s no longer supported in many (most?) modern cards. I know ApplePay refuses to do it. I think card brands have said to stop using it but I’m not positive.
The other mode (absolutely dominant in contactless) works through encrypted EMV tags the same as you get when using a physical slot. The order of things is a little different but it’s just as secure.