If you're talking about the openledger wallet there's not really a 'log-out' button. Just a lock in the upper right corner that locks the wallet from having any activity until you enter the password again. 
Dan built the Bitshares  blockchain and code (which is beautiful), not so much the wallet (which really is very very good). 
Coinbase has a different sort of function to OpenLedger. Coinbase lets you trade your dollars for bitcoin and then holds the bitcoin private keys for you. They basically issue you an IOU for your hard-earned dollars. OpenLedger is an interface to the Bitshares blockchain and you get to hold you own key to your own assets. OpenLedger also lets you trade a variety of coins like Steem or Etherium and other assets like Gold, USD, or Obits. 
Coinbase makes it simple, they offer one price and one trade pair with a spread that they choose. This is extremely profitable for them. OpenLedger offers better flexibility and infinitely better security.