Jazz covers a wide variety of styles, from ragtime and Dixieland to swing to bebop to alternative - and a whole lot more in between. The focus is always on creativity and improvisation - sometimes if is difficult for a new listener to even follow where the original melody goes, when players start improvising on it! Similarly, the rhythmic and harmonic structures, which started out as part of the accompaniment, are also expected to leave the normal world behind, and take off into flights of fancy. So not only is somebody redecorating the rooms - the whole house has moved to another state.
Blues tends to be more adherent to its roots,especially in its use of phrase and chordal structure. Like barbecue ribs, however, each major city had it variations on that formula. But in its essence, 12 bars, 3 chords. This makes is easy to follow, and the lyrics are slower and they repeat - so it is easier for the audience to keep up.
Musicians have an old joke that reflects on the contrast - and the relative popularity - between traditional blue, and progressive, atonal jazz:
"What is the difference between blues, and modern jazz?"
"A blues musician plays three chords, in front of thousands of people. A modern jazz musician plays thousands of chords - in front of three people."
The Ella and Frank things you are hearing are 32-bar standards; Frank may deviate from the melody some, and add his own phrasing; Ella will do that, and also in up-tempo tunes, she will "scat' - use her voice like an instrument, using no words, but free syllables that allow her the freedom to improvise melodic passages just like an instrumentalist would do. Although not invented by her, she was the queen of this skill.
If you can get it - and sit thru it all - get the Ken Burns series on jazz as a video (several in a box). you will learn a ton. Also watch the HBO series Treme. Go to the Jazz at Lincoln Center site - and watch shows in which Wynton Marsalis talks about jazz as well as playing. You have a lot on your plate - but it is all tasty.