Early today I had a message that my gas cap was loose. I was going try tighten it when I stopped, but forgot. Later my engine light came on after I ran my car through car wash. I remembered about about the gas cap and tightened it. Started car and engine light still on. Is there any connection here?
It could be connected, but without knowing what the code is behind the check engine light (CEL), there's no way to tell. That said, I'm doubting the two are connected. If the dash readout told you specifically the gas cap wasn't tight (or isn't sealing), it would have either continued to tell you the same or would have turned off if it is re-secured.
If it was the gas cap which caused the CEL, it takes a little while for it to turn off. The computer does its checks and discovers the gas cap is back in place, it will then turn the light off, though the code will still be stored.
Take your vehicle somewhere and have the codes read. You can have it done for free at most major chain auto parts stores.