I know that a state funeral is when the body lies in state for some period of time before the burial. However, the Queen Mother is going to be lying in state yet they are not calling it a State funeral. It is called a Ceremonial Funeral. What distinguishes a state funeral from a ceremonlial funeral?
The distinction you are referring to is that between a state funeral and a royal funeral. The technical distinction is that a state funeral is organised by the Earl Marshal while a royal one is organised by the Lord Chamberlain of the Household.
A state funeral is reserved only for the monarch (a king or a queen regnant - the Queen Mother was, of course, only a queen consort) or the most distinguished of public figures. The only person in the UK to have been given one in the twentieth century, apart from monarchs, was Churchill. This involves a gun-carriage, a public lying-in-state and a public funeral service, either in St. Paul’s or Westminster Abbey. In the case of a monarch, there is usually no public funeral service in London, but a very grand commital at Windsor.
A royal funeral is reserved for members of the Royal Family and covers any number of permutations. Princess Margaret’s funeral was an example of a low-key version. The Queen Mother, on the other hand, is to receive the very grandest form of the ceremony, which will, in most respects, be indistinguishable from a state funeral. Many of the practical arrangements for the funeral for Diana, Princess of Wales, were modelled on those for the Queen Mother, partly because Diana’s death was unexpected, although there was, of course, no public lying-in-state and a deliberate decision was taken to play down the military elements.
Just to confuse things further, distinguished ex-soldiers, such Earl Haig or Viscount Montgomery, are sometimes given a very grand military funeral, which can share some of the features of a state funeral. One could argue that this is what Mountbatten received, although, as a member of the Royal Family, it was officially a royal funeral and many felt that it was a state funeral in all but name.