The thing that we call the 1939 Register was created by the enumeration in September 1939. A new set of books was then created for anyone born in England and Wales, or arriving from elsewhere, or being demobbed from the armed forces after that date. Collectively, all these books were called the Central Register, in use up to 1991 when the NHS computerised its records.
ScouseBoy is right to say that there were many registers. Each Local National Registration Office kept a register for its own area, in the form of a card index. Updates were made to both the local registers and the Central Register, but they were not identical; for example, changes of address were only recorded in the local registers, but markers relating to people who had failed to attend when called up for military service were only noted in the Central Register. That's a somewhat over-simplified version, but you get the drift!