You can buy BTC in binance and sell it in bittrex. But of course you still need to send your Binance funds to Bittrex to do so. TabTrader isn't like a global wallet for exchanges or something. TabTrader just sort of allows you to manage multiple accounts of multiple exchanges. Not sure if I would trust it though, as I haven't done my research on it. Binance has it's own app by the way, both on Android[1] and iOS[2]; just so if you didn't know.
[1]
https://play.google.com/store/apps/details?id=com.binance.dev&hl=en[2]
https://www.binance.com/ios-install.html