I do think Coinbase and GDAX are the same company.

What's the Deal with Coinbase and GDAX?
Coinbase announces GDAX providing Coinbase users additional capabilities

The birth of GDAX
Additionally, the company recognized that the capabilities for this exchange were beyond what was needed for the individual, more "casual" user of Bitcoin so they decided to rebrand this Exchange as GDAX - Global Digital Asset Exchange- to not only highlight the added capabilities but the worldwide focus that the exchange provides to traders. They also provided access to Ethereum through this exchange to satisfy the growing demand for that cryptoasset.

Coinbase's White points out the company built GDAX from the ground up. He feels that although there are many smaller exchanges that trade many cryptocurrencies worldwide on a daily basis, Coinbase is in a leading position because of its integration with regulatory concerns and its past success as the leading exchange for Bitcoin and now for Ethereum as well. "We believe exchanges that provide advanced trading features and meet regulatory requirements are most likely to succeed long term,” White says.

Mid-year of 2016, the company made the decision to rebrand the Coinbase Exchange part of their business quest to be the world’s largest exchange and expand its international footprint.

https://www.thebalance.com/whats-the-deal-with-coinbase-and-gdax-4063868 The whole article can be found here. Thank you for the post! Good info upvoted! Will Resteem!!