Which was first communism or marxism. Was communism conceived from marx's ideas or was it the other way rround?

"Marxism" neither precedes nor succeeds communism, since they are two different concepts. Marxism is an ideology based on all of the theories of Karl Marx. Communism is an economic and political system. According to Karl Marx, socialism precedes and eventually evolves into communism. The idea that socialism will evolve into communism is only one of the aspects of the ideology known as Marxism. There are many more aspects to "Marxism" than just socialism and communism.