Here is a photo that illustrate the difference; the black one, on left, from Desert Tactical SRS, is push feed (henceforth referred to as PF) and the silver one, on right, from Whitworth Express Mauser, is controlled round feed (henceforth referred to as CRF):
Note that the PF design uses button type ejectors (the pictured one has two for redundancy, most have one) that are set into the bolt face, while the CRF design uses a blade (not sharp) built into (or bolted onto) the receiver to eject the casings. You will also note that the PF extractor is rather small compared to the large "claw" of the CRF design. This is hinged to allow it to snap over the rim, whilst most CRF designs are incapable of this function (making single-feeding difficult).
FWIW I prefer the CRF for hunting and the PF for target shooting, et al. The CRF is a bit more reliable and can be used inverted, but the PF allows for greater versatility. As noted the CRF bolt can be thrown slowly to "dribble" the cases out in a neat pile, or thrown with authority to ensure that the case ejects well clear of the port (and often several yards away), the PF design will throw cases to the same relative point each time.
To complicate things a bit, there are some hybrid actions that use a CRF claw, but have a ejector built into the bolt face like a PF. There are also PFs that have a fixed blade ejector rather than buttons set in the boltface, but the action is always classified by the method of insertion/extraction, not the method of ejection. If it "controls" (holds) the cartridge throughout the cycle it is CRF, otherwise it is PF.