This is an old article, but it remains an interesting topic:
CHAdeMO General Assembly Contemplates SAE Plug Competition - HybridCars.com
We don't (yet) know if Model S will ever support use of either of these types of offboard DC quick charge systems.
Some related old threads:
DC Quick Charge vs Supercharge
Likelihood of a CHAdeMO adapter for the Model S
Will other brand vehicles be able to use the Supercharger?
TEPCO/CHAdeMO Level III charging station/connector
Charging Station standards
What charge port connector?
SAE announces the 'official' charging plug standard for North America
New Model S owner charging primer (US)
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J1772 beat out its main rival, the Japanese CHAdeMO plug (which is also available as an option for the Nissan Leaf and is used in over a thousand chargers installed in Japan), along with Tesla’s proprietary Supercharger system. Whether the SAE standard will see an end to these rival plugs or the beginning of an automotive version of VHS versus Betamax remains to be seen.