I think, as others have already said, that the solitaire game described in the original post is called "Klondike". It's the solitaire that I learned as a boy.

I once had a computer program for an alternate solitaire called "Canfield", which I enjoyed very much. However, I haven't been able to learn how to deal this game "by hand", with actual cards. I have tried doing a google search on "Canfield", and I get plenty of hits, but none of the sites explain how the game is dealt in such a way that I can understand it. Probably my fault, rather than the sites, but it's still frustrating.

Don