Synoptic scale vorticity is analyzed and plotted on the 500-mb chart. Vorticity is a clockwise or counterclockwise spin in the troposphere. 500-mb vorticity is also termed vertical vorticity (the spin is in relation to a vertical axis). This vorticity is caused by troughs and ridges and other embedded waves or height centers (speed and directional wind changes in relation to a vertical axis). A wind flow through a vorticity gradient will produce regions of PVA (Positive Vorticity Advection) and NVA (Negative Vorticity Advection). PVA contributes to rising air.
Vorticity caused by a change in wind direction or wind speed with height is termed horizontal vorticity (the spin is in relation to a horizontal axis). Horizontal vorticity is most important in the PBL (low-levels of atmosphere). i.e. If the wind at the surface is southeast at 30 knots and the wind speed at 700 mb is west at 60 knots, there will be a large amount of speed and directional (veering) shear with height and therefore a large amount of horizontal vorticity.
Streamwise vorticity is the amount of horizontal vorticity that is parallel to storm inflow. Storm inflow is the velocity of the low-level wind moving toward a thunderstorm. Helicity is the amount of streamwise vorticity that is available to be ingested by a thunderstorm. Helicity is a great chart to use to assess horizontal vorticity and the threat for rotating thunderstorms.
In summary, vertical positive vorticity contributes to upper level divergence in the PVA region and thus rising air while horizontal vorticity is important to severe weather (large values of horizontal vorticity lead to large values of Helicity, which increases the likelihood of tornadoes in association with supercell thunderstorms). Both vorticity types are a clockwise or counterclockwise rotation, but one is in relation to a vertical axis and the other a horizontal axis.