I agree it is incredibly complicated and it took me about a day of working through some 3 years ago when I tried to get my head around it.
The Basic State Pension is the thing that gets talked about so much in the news. It depends on NI contributions, and from next year one needs at least 30 contribution years to get the full amount. Otherwise it is a proportion. When can draw it is the other topic in the news - 65 for men, 60 for women but rising progressively to 65 also from April 2010. It is this 65 age that is in the news right now as it will rise in time - 68 has already been announced.
If one is 'contracted in', one also gets an additional pension from the state. This starts from the same date as the state basic pension, and depends on earnings. It used to be called the SERPS scheme, but is now called the Second State Pension. The Pensions Service maintains the contribution record of individuals and you can get a pension forecast of the combination of Basic plus Additional (SERPS+2SP) through the DirectGov website.
If one is 'contracted out', one gets one's additional pension via a private sector provider. Getting forecasts from this can only be done from the company providing it. When people talk about 'pension pots' these are the sums of money held by the investment companies on an individual's behalf that will provide the pension. When one draw this is up to you (there are Government and scheme rules about the minimum age when it can be drawn)
Most people will get their pension from various sources - not necessarily starting at the same date.
Many years ago (1970s and earlier), there was a scheme called 'Graduated Pension'. This was the predecessor to SERPS and older people may find some entitlement to a bit extra from it. The Pension Service maintains the individual record on this scheme and it is included in pension forecasts.
See here for more general info about these schem