Postgraduate taught is usually a Masters degree (MA) but there are other variations depending on what subject you want to take, and this usually takes place over a year full time.
A Postgraduate research degree however normally results in a Phd, and requires the researcher to engage in independent research over three or more years. You usually need a Masters degree (or significant experience in the field or research) to apply for one of these. You also need to submit a research proposal and have research training, if you hope to be accepted :)