cox.net vs cox.com

Functional difference?  Who knows?

The com and net are different domains but I don't know if each has different IP addresses.

When Cox decided to become an ISP in 1995, Cox bought a block of IP addresses and registered both domains (com and net).  Cox either did this because com and net are the big root domains so Cox probably registered both to protect its brand name...or Cox wanted net for in-house and com for subscribers.  Again, who knows?

However, networks don't speak domain names.  Networks speak 1s and 0s (IP addresses).  If you type cox.net, a browser doesn't understand...has to request a translation...and a Domain Name Server translates the request into an IP address.

Since you're a subscriber, outside the in-house domain of Cox, with a public IP address; your request goes to the public DNS server of Cox...as opposed to its in-house private DNS server.  In the public DNS server of Cox, both com and net requests are annotated to go to the com domain.  Try it.  Type cox.net and you'll be directed to cox.com.  If you're an in-house employee at Cox, however, a cox.net request may go to an internal, private website.

Any functional difference to you?  No...because both your public requests will go to the same server.