What is the full name of 中央军委? According to my research, I find there are two institutions in China now which might have the shorter name as 中央军委, one being 中华人民共和国中央军事委员会, the other being 中国共产党中央军事委员会. Both of the bodies might be made up of the same and exact people, but it is unusual or impossible to have the same shorter name for two different bodies.
They're the same organization in fact.


  中央军事委员会与中国共产党中央军事委员会事实上是同一机构两块牌子，不是合署办公。对武装力量发布的命令一般仅使用中国共产党中央军事委员会名义、或以中央军委的作为统称。与中华人民共和国国务院联合发布命令是使用中华人民共和国中央军事委员会的名义。


(中央军事委员会 and 中国共产党中央军事委员会 is the same organization with two plates in fact, but not merging work in one official. Orders to armed forces are usually issued under the name of 中国共产党中央军事委员会, or 中央军委 as the general name. When orders are jointly issued with 中华人民共和国国务院 (the State Council) the name of 中华人民共和国中央军事委员会 is used.)

See 中共中央军事委员会和中华人民共和国军事委员会有何区别