Murder really only has 2 degrees although some people note that there are 3 degrees of murder which is somewhat true.
3rd degree murder is basically manslaughter under the law which is sometimes treated differently than just plain murder is.
So that is why there is no 3rd degree murder even though manslaughter is the killing of a person and killing people is murder.
But according to law there are 1st degree and 2nd degree murders.
1st degree murder is murder that is premeditated for example the person is stalking someone over a few days and plans their murder.
2nd degree murder is murder that is done without plan and done in the heat of the moment.
Manslaughter which is also murder is the crime of killing a human being without malice aforethought, or otherwise in circumstances not amounting to murder.