Ok Bob, here goes:
PUSH FEED.
In this design, when the bolt moves forward and pushes a round up out of the magazine, the round is loose. The bolt pushes the round into the chamber, then the extractor snaps over the rim. If, before the round is chambered, the bolt is moved back, the round just lays there, since the extractor hasn't engaged the rim. Most modern rifles use this system.
CONTROLLED FEED.
In this design, when the bolt moves forward and begins to push a round up out of the magazine, the round is immediately caught and held by the extractor. The round is not free, and is held by the extractor until it is ejected.
The Mauser rifles, most older designs, and most pistols use this system.
Both work equally well. Some people think the controlled feed better, since it is much more difficult to have a "double feed" situation. With the push feed, if the bolt isn't closed over the chambered round, allowing the extractor to engage, opperating the bolt will attempt to feed another round, causing a jam.