Don't know if this means anything but I have a book called "Sailing Fundamentals" that is "the official learn to sail manual of the asa and the uscg auxiliary". Don't know if there's anything between the two except that maybe they both happen to like this book. Might be the old seventies show photos and illustrations.
The uscg will be the ones to save you're butt in blue waters if you get into trouble so if they're using the same book as the asa then I would start there. You can always take any other courses you want in the future.