I am a little confused about whether the images to be stacked are all taken at the same shutter speed, aperture and ISO or is it similar to HDR, in that I would need to take several different exposures?

If your intent is to reduce noise, you generally stack images that were taken with the same parameters (exposure time, ISO, etc) in succession. The idea is that with a single very long exposure, so much noise may build up in some of the sensor's photosites that it degrades the image, so you instead break that exposure up into a number of shorter ones, and then use software to combine the images into one, resulting in a less noisy image.

You're right that HDR is similar, but in that case you're sampling the scene with different parameters in order to capture more dynamic range than the sensor can capture all at once. Another example is focus stacking, where you take several exposures with slightly different focal points, and then combine the sharpest parts of each image to get more depth of field than you could manage in a single image. This is useful for macrophotography, where you're photographing something very close to the lens and therefore get very shallow depth of field even with small apertures.

So, these are all forms of image stacking, but the parameter that's changed for each exposure depends on your objective. For noise reduction, the parameter that changes is time -- you're slicing up the single long exposure into shorter segments and recombining them.

Consider that another reason for image stacking in astrophotography is to get the effect of a long exposure without star trails -- stacking software meant for astrophotography can align multiple images to eliminate the circular trails caused by the Earth's rotation that you'd get in a single long exposure.