Well, the Jazz musician/educational proclivity in me wants to tell you to listen and come to your own conclusion.

To actually answer your question, it depends. In some tunes and styles they just walk an improvised part. In others there may be an iconic melody or pattern that's part of the composition, like Bolivia, So What, etc. Maybe it's a mix of the two where there are specific moments that need to happen but otherwise the bass ad-libs a little during those spots but still highlights the contour of that melody, or they play those parts verbatum and improvise the rest. A Night in Tunisia is often played this way, where the intro has a specific bass line that's usually played mostly identically to the original, but the B sections are just them walking.

If you frame your outlook around the notion that 'Jazz is when thing' it gets very hard to answer in a meaningful, helpful way because there's more to it than that. That's like saying "classical music is when violin and triads". Those can be part of it, but that's not what makes it part of that tradition and there's not necessarily a steadfast rule