Bitfinex was founded in December 2012 as a peer-to-peer Bitcoin exchange, offering digital asset trading services to users around the world. Bitfinex initially started as a P2P margin lending platform for Bitcoin and later added support for more cryptocurrencies.
In 2015 the exchange's customers were hacked, losing about $400,000, and in 2016 about $73 million more was stolen from its customers' accounts. [source]
Binance is a global cryptocurrency exchange that provides a platform for trading more than 100 cryptocurrencies. The company was founded in China but moved its servers and headquarters out of China and into Japan in advance of the Chinese government ban on cryptocurrency trading in September 2017. As of January 2018 it was largest cryptocurrency exchange with a Binance coin (BNB) market capitalization of $1.3 billion. [source]