That was the popular one when I grew up, the "pump." Supposedly, it shot harder. I couldn't tell any difference, but it was widely believed to be true. It also, IIRC, loaded differently. Had a sort of tubular magazine instead of just pouring the BBs down the hole in the barrel cover.

I had a "Long Rifle" Daisy BB gun, from back in the Davy Crockett craze. It had the "Rules of Fair Chase" modled on the buttstock.