According to the Toyko Olympics page for the skateboarding events, the park event is a more bowl-related course.
Park competitions take place on a hollowed-out course featuring a series of complicated curves – some resembling large dishes and dome-shaped bowls. From the bottom of the cavity, the curved surfaces rise steeply, with the upper part of the incline either vertical or almost vertical. Among the attractions of park competitions are the immense heights achieved by climbing the curves at speed and performing amazing mid-air tricks.
And to compare against the street event, you are correct that it takes place on a straight street-like course.
This competition is held on a straight ‘street-like’ course featuring stairs, handrails, curbs, benches, walls and slopes. Each competitor performs individually, and utilises each section to demonstrate a range of skills, or ‘tricks’. Judging takes into account such factors as the degree of difficulty of the tricks, height, speed, originality, execution and the composition of moves, in order to award an overall mark.