When in doubt, look at the airlines' websites or wikipedia.
These are two completely separate companies.
They have very different mileage programs. Virgin America's is based on spend, and there are far fewer partners. Virgin Atlantic has more partners, but high redemption fees. You can also credit Virgin Atlantic to more airlines (e.g., Delta).
http://www.virgin-atlantic.com/us/en...n-america.html
For a Virgin America roundtrip flight in Main Cabin (Coach) from SFO to JFK, you would earn 2586 Virgin Atlantic miles. In Virgin America's Elevate program, you would earn 5x the price of the ticket.
https://www.virginamerica.com/cms/el...irgin-atlantic
For a Virgin Atlantic flight roundtip from London to JFK, you would earn 690 Virgin America points in most economy tickets. As a comparison, you would earn 6916 Virgin Atlantic points.
So it really doesn't make sense to credit any Virgin Atlantic Flights to Virgin America's Elevate program.
But redemption levels are also different. Look at each program and see what you can spend miles on.