A Polarizing filter (usually circular) is mainly use to reduce the glare or reflections from non-metallic reflective surfaces like water or glass. It also reduces the exposure but mainly use to saturate the colors and enhance the clarity of image. It works best when you are right angle to the sun light. Polarizing filters are not normally used for a wide-angle shot that includes the sky, as you'll get a very uneven sky tone due to the wide range of angles of the light entering the lens. Neutral Density (ND) filter is use to reduce the overall exposure uniformly giving an uniform reduction in light across the frame without affecting the color. ND filter is commonly used in a situation where it is bright sunny light and using a wide aperture to get a shallow depth of field would result into overexposed image. It is probably more popular to use when you want to use the slow shutter speed to get the cloud effects or milky effects of the water with a long exposure which could possibly overexpose your image without using ND filter.
There is another type of filter which you could possibly be confused with ND filters and that is called Graduated Neutral Density filter, also known as a Graduated ND filter, split neutral density filter, ND grads, GND, split ND or just a graduated filter. It is use to reduce the light over the part of the frame but not the entire frame and mostly used in a holder which gives your the flexibility where you want to darken the frame and where not. The Graduated Neutral Density filters are much more common in a landscape photography where you can darken and add details to the sky and maintain the correct exposure to the foreground at the same time.
Usually Graduated Neutral Density filter comes in two types and they are:
1. Hard edge
2. Soft edge
A hard edge is used when there is an abrupt change in brightness; for example a field with a horizon to a bright sky (good for seascape shot). A soft edge is a wider smoother change from light to dark. This is used when the light and dark portions are not distinctly separated; for example a mountain and sky. A soft edge filter is less noticeable than the hard edge. It also has the benefit of making the sky more intense by darkening the sky closer on the top of the frame.
Even though a polarizer and ND Grads can both be used to darken and add detail to the image but they work quite differently. A grad filter works same at any angle to the sun whereas a polarizer works most strongly at 90 degree angle to the sun. As I already mentioned, a polarizer can produce some strange variations in the sky tone when used with the wide angle lenses or an ultra wide angle lens, whereas ND Grads have the same effect across the frame regardless of the lens type. Also graduated filter only darkens an area of your photograph which you can vary according to how you slide the filter up and down in the holder (may not be the case if you use circular grad filter though).
These days, many photographers try to replicate the effect of the graduated filters by using bracketed exposure shots and post process them using software but you can't do everything that polarizer does in the post processing. Some people prefer to add-in a grad effect using software but if you have already blown out the details in the original photograph, there is no way to get the details back during the post processing. If you do not want to use the grad filters, you can shoot in a RAW format and take 3 or 5 or more automatic bracketed shots and merge them (or create an HDR image) by using the Lightroom.