“Does the jetstream move high and low pressure systems or do they move the jetstream?”
The quick answer is the jetstream and surface high and low pressures move together, but without the jestream the surface systems would weaken and die out. A surface low pressure is air converging and it has nowhere to go but up! Diverging air aloft in the jetstream provides continued lift and removes the air from the surface allowing the surface low to continue to build. The opposite is true for a high pressure system; a surface high is air leaving the center of the high and convergence of air in the jetstream aloft allows air to sink. Rising air from a surface low often leads to stormy weather whereas sinking air in a high pressure often provides calm, sunny weather.
The more North to South wobble of the jetstream the more extreme the weather, why the east coast is cooler and stormy right now in a low and we’ve been so hot on the west coast. We’ve also been humid because the flow around the high is clockwise which is ushering in monsoon moisture. The high pressure the Pacific Northwest typically has is a high pressure off shore which ushers in drier cool air from the west.