You know despite trying to describe them differently you confirmed than I am correct. They are one and the same.
The problem with just making it up as you go is that you are almost always going to be wrong...as you are in this case.
The science behind the polar vortex | National Oceanic and Atmospheric Administration
"The term vortex refers to the counter-clockwise flow of air that helps keep the colder air close to the poles (left globe). Often during winter in the Northern Hemisphere, the polar vortex will become less stable and expand, sending cold Arctic air southward over the United States with the jet stream (right globe). The polar vortex is nothing new – in fact, it's thought that the term first appeared in an 1853 issue of E. Littell's Living Age. "
NOAA states clearly that the vortex sends cold air south WITH the jet stream....not as the jet stream...not anything that would lead anyone who has read the first word of actual science on the topic to believe that the two were one in the same...but WITH the jetstream.
Here...from Stanford University...
Polar vortex: The science behind the cold
“When the polar vortex splits into two, the jet stream moves south over the Atlantic basin, and it takes all of the storms with it,” said Sheshadri, an assistant professor of Earth system science in Stanford’s
School of Earth, Energy & Environmental Sciences (Stanford Earth). “We have no idea during a given event exactly when the storms might strike, but on average you see impacts for a month or two after the vortex splits.”
Again, a clear statement that the polar vortex and the jet stream are two different things...one can most certainly have an effect on the other..but they are distinct and different things.. Do you never tire of being wrong?