The most common way to phrase jazz eighth notes is to articulate every other note as in measure 18. But at the slower tempo of Joe's Thing, it is also common to articulate every note as in measure 38, or different combinations of notes as in measures 29 and 30. When the phrasing is varied in this way, it makes the interpretation sound more interesting, musical, and less mechanical. But again, it is something you have to hear and absorb. Triplets provide a lot of energy to a melodic idea and can also be phrased differently, as in measures 6 and 21.
Sixteenth notes are the least varied in terms of phrasing because of their speed.
These usually have every other note articulated or slurred throughout, even though a combination of the two is used sometimes, especially at a high point of a phrase, or at an ending of a phrase. Many players highlight some notes in a phrase by articulating them harder, and using a softer, more legato articulation to give a phrase a smooth, silky kind of feeling. If you are interested in learning more about phrasing and articulation, you may want to check out Jim's etude books, Jazz Conception, published by Advance Music. Many of the phrasings and articulations are indicated. The etudes start off fairly easy and gradually become more difficult.