Notice the repeating patterns of notes in the last example. These patterns are called riffs. A riff is a short musical idea (usually one or two bars long) which can be altered and varied to fit a chord progression.
The use of riffs is very common in saxophone playing. Riffs can be used in a variety of situations including playing as part of a horn section, filling in behind a vocalist, and soloing. The following two examples are a riff style of playing applied to the 12 Bar Blues progression.