The bottom clamp-on style is designed with two half domes, each with a half-circle opening where the domes are connected (in a hinge-like fashion). Either one or both of the half-domes have a loop attached for connecting the strand to the clasp. When the half-domes are closed, the half circles form a complete circle, surrounding the cording or thread and the two half domes form a sphere to conceal the knots or crimps.
Each of these styles needs to be incorporated into the original design of the strand, as the stringing material needs to pass through the hole in the bottom of the bead tip.
Side clamp-on style, like the bottom clamp-on style, has half-circles on each half-dome to allow for the cording, as well as loops to connect the bead tip to the clasp. The difference is that a side clamp-on bead tip can be added after the design has been strung, as it comes in from the side.