What is the difference between playing blues piano and jazz piano?

As Ethan states, blues is a huge component of jazz. However, blues, for the most part, occupies somewhat limited harmonic and formal territory - speaking very generally here, it utilizes a 12 or 16 bar form, basically I, IV and V chords, and the blues scale. Blues is also somewhat idiomatically locked into certain historical archetypes; that is, if you don't do things in the familiar way, it would no longer be considered authentic "blues." With jazz, on the other hand, the form can be anything, the harmony can be anything, and the strictures of meter, feel of 8th note, or world/ethnic origin go out the window. There are certainly standard forms and harmonic progressions to be sure, but it is accepted and encouraged to operate outside of those as well as inside them. From a purely practical standpoint, a jazz pianist is simply more versatile than a strict blues player. If one seeks to be a professional musician, I would not recommend limiting my skill set to just the blues, as all you're doing is limiting your opportunities to make music in different situations.

Jazz players have more fingers :))