Absolutely correct. 3 factors to exposure: ISO, aperture, shutter speed.
You can think of exposure as filling a cup.
-Aperture is the size of the opening letting light (water) in.
-Shutter speed is how long you let the light / water flow in.
-ISO is how big the cup is. A high ISO (like ISO 1600) means the sensor/film is very sensitive to light. So you need less light to make a proper exposure, thus it's a small cup.
Now say we have a given ISO. For some aperture, there is always a corresponding shutter speed that will precisely fill the cup (give you the proper exposure) and vice versa.
So in shutter priority, you tell it how long you want the light coming in, and the camera will choose the right aperture.
In aperture priority, its the opposite: you tell it how big you want the hole of light coming in, and the camera will choose the length of time to let it in.
You (or the film) chooses the ISO in both cases.
Aperture priority is usually more useful unless you have a specific speed you want (usually for creative long exposures). If you want the fastest shutter speed possible, then just set the aperture to be the widest the lens will permit it to go.