Yes, the same company runs all these different airlines' dining programs. It is called iDine. However, you are able to register a different credit card with a different dining program. For example, my visa is registered with British Airways Dining; my mastercard is with American; my Amex Starwood card is with iDine; and my Delta Skymiles card is registered with NW Dining.
You can earn additional miles if you eat at the restaurant more than once a month by not using the same credit card twice in that month. However, your miles will be posted to the different carriers rather than to just one.