According to this Campaign for Nuclear Disarmament backgrounder, CND’s symbol was the one below, which became commonly known as the peace symbol.

These badges

were made by Eric Austen of Kensington CND using white clay with the symbol painted black. Again there was a conscious symbolism. They were distributed with a note explaining that in the event of a nuclear war, these fired pottery badges would be among the few human artefacts to survive the nuclear inferno.

The Museums Victoria, though, has another symbol which appears to combine the CND initials with the title of a Crass song.

The initials CND are printed across this badge, signalling that it was initially made for the British organisation Campaign for Nuclear Disarmament. However, the donor of this badge, Nic Maclellan, thinks that it might have been re-issued in Australia using the British original design. The badge relates to a 1978 song by Crass called Fight War not Wars, in which this line is repeated over and over again.

I shall not try to understand the relationship between these two symbols, but I found this interesting.