GDAX is just Coinbase's dedicated exchange. On Coinbase you can buy and sell BTC/ETH/LTC with USD, although transactions take a couple of days to go through (last I checked). Its meant for consumers and investors. GDAX is a complete exchange, targeted at traders, where you can trade between a variety of pairs (BTC/USD, ETH/USD, BTC/GBP, ETH/BTC), somewhat similar to a foreign currency exchange.
The fee structure for Coinbase's main site and GDAX are different.
so coinbase fees apply to withdrawing to your bank account or card ("cashing out")
but the actual trading fees if you keep the money in their system (GDAX's) are much lower, right? Like around .25%?
Yeah, there is a flat transaction rate on Coinbase, but GDAX fees are charged based on if you create liquidity (maker) or take liquidity (taker) off the book. On GDAX, makers are charged an effective 0% fee on trades, and takers are charged 0.25% (but you get issued a rebate if you account for a lot of volume).
So in reality you can get money in and out of GDAX without getting charged any deposit/trading/withdrawal fees if you create liquidity by placing limiy orders.