"In-network" is an insurance term meaning basically "we negotiated preferential deals with this doctor, so it's in our best interests to steer members there." (There are more complicated technical definitions, but that's the upshot.) From where you sit, the only thing that matters is what they already told you - in-network means they pay 80% + copay, out-of-network means 60% + copay. So you have an incentive to find an in-network doctor, but they will still pay a huge chunk regardless, which is cool. (You may want to clarify whether it's limited to US doctors/surgeons; they may pay zero for someone out of the US.)
The only real way to find out whether a doctor is covered, and how, is to contact that doctor's office and ask. This is true in general, not just for surgeons. I know someone who swears Dr. Rumer in Philly takes a bunch of different insurance plans, but she had Blue Cross so I don't know offhand about Aetna. The good news is that I think these days you can email them all, so you really only have to put together a very simple query ("Do you take Aetna Plan X, and if so, do they consider you in-network for them?") and draw up a short list from whichever ones say yes and/or yes.
I am not a professional nor do I play one on the internet, but I have spent a LOT of time arguing with insurance companies. Be persistent, if the doctor says they are covered and Aetna refuses, and find out directly which precise hoops they want you to jump through.
