I don't really think that Generals had a story line. The "plot" were a series of excuses why the battles where taking place in China, Kyrgzstan, Kazakhstan, etc. If everything was set in China (maybe Sinkiang, with all the muslim influence) or in its periphery, the game would be largely identical.
Red Alert definitely had a plot, though I can't say I was too thrilled. For one, I'd have liked to see Soviet and American armies dueling it out on nuclear wasteland after a nuke exchange.
And overseas invasions of America: well, let's say they're very implausible for the 20th centuries.