The difference between a state funeral and a ceremonial funeral is that a state funeral has to be voted for in parliament. There's no difference in ritual between the two (ceremonial funerals may include a lying in state) except that in a ceremonial funeral the gun carriage is drawn by horses and in a state funeral by sailors. This latter tradition dates from an incident at the funeral of Queen Victoria when the horses bolted and a bunch of naval ratings took their place.
Here's a list of all the non-royal state funerals since time began.
- Sir Philip Sidney (1586)
- Admiral Robert Blake (1657)
- Sir Isaac Newton (1727)
- The Viscount Nelson (1806)
- The Duke of Wellington (1852)
- The Viscount Palmerston (1865)
- Lord Napier of Magdala (1890)
- The Rt Hon William Gladstone (1898)
- The Earl Roberts of Kandahar (1914)
- The Earl Haig (1928)
- The Lord Carson (1935)
- The Rt Hon Sir Winston Churchill (1965)