The two exchanges are essentially the same, with the main difference being that Coinbase Pro is a slightly improved version of GDAX. Since they are fundamentally the same product, you can see our page on GDAX for how Coinbase Pro functions.
Moving forward one should use Coinbase Pro and not GDAX for their Coinbase-run trading platform. With that in mind, balances on one exchange will show up on the other and GDAX directs you to Coinbase Pro when you go to that site.
TIP: You can use the same logins for Coinbase, Coinbase Pro, and GDAX.
TIP: Starting in 2020 Coinbase Pro began to allow margin trading.