I don't think there is any jazz version of harmonic minor, it's the same as a classical harmonic minor-an aeolian (or minor) scale with a raised seventh degree.

Are you thinking about the jazz melodic minor scale? The jazz melodic minor is just the ascending form of the melodic minor scale without the descending component. Jazz musicians often call this scale an Ionian flat 3 because it's a major (or in modal terms-Ionian) with the third note flatted.

In classical music theory, these scales are played as natural minor when played in descending order. The jazz version would mean the notes stay on the same scale degrees regardless of the direction the scale is played.