A friend asked me how I would explain jazz to someone who wasn't a musician, analogy was pretty much the only way to approach it, for me. I said to her that most rock music, Western classical music, etc. was very much akin to a play - the various actors do the same lines and the same action with the same sets and costumes every time that play is performed and they try to communicate meaning and emotion to their audience with their interpretation of character, invoking the feelings and emotions of each character in such a way that the audience feels it in a very real and visceral way. and if you send a copy of that play to another group of actors, they can put their own "spin" on it , but the words and the actions are the same, they don't change.
Blues, and some of the rock and country music that has at its base the blues, bluegrass and a few other forms of music in this country are akin to telling stories - the basic plot and characters remain the same, but the details, perambulations, digressions, etc. all depend on the skill, life experience, and the ability of the storyteller to speak to his/her specific audience; some audiences want long, detailed stories, some just want to hear how it all worked out.
But jazz, particularly post-bop jazz, is much more akin to a conversation, a deep conversation, in which the direction of the conversation can twist and turn and embrace a multiplicity of subjects and directions all surrounding and relating to, and ancillary to whatever the original topic of conversation happened to be. All contingent on the depth of knowledge, breadth of vocabulary, and most importantly the intent of those who are involved in the conversation.
The basic premise for playing is this - you have a melody. That melody is supported by a harmonic framework (the chord progression), that the composer chose. When you hear those two things, what do YOU hear that you want to play in response? Yes, the bass is there to supply the foundation for the other instruments, but your line should be a melodic response that defines the harmony AND propels it forward to the next chord. And the next and the next. My former teacher described it with the analogy of learning to drive; when you start out, you aren't really looking much past the windshield and the car in front of you. When you get some experience, you're not looking at anything, you're seeing the whole picture - the car in front of you, the cars ahead, the intersections, what's behind you, etc.
So, sure, scales, arpeggios, yada, yada. That's not vocabulary, that's getting some familiarity with the instrument and working out solutions to fingering and position shifts. The skill set that really means something is to be able to HEAR those things with enough clarity that when you hear that song that you can play the roots to, you can hear not only what the chord quality is (what those other notes are), but you can hear internally what notes you want to play as a response and where those notes are on your instrument. As I've said before countless times, the 3 legs of the tripod are TECHNIQUE (physical approach to the instrument, how to play without tension) UNDERSTANDING (music theory, how functional harmony works) and HEARING ( ear training, being able to identify, sing, and play the intervals, triads, chords with tension etc.).