I have been flying for about 2 1/2 years and gone through lots of planes. I know about CG and how important it is to flying a plane successfully. My question stems from terminology. I hear people talking about moving CG and I get confused.

If I have an airplane that is perfectly balanced and I move the CG forward, won't that make a plane tail heavy, since I am moving the point to which the plane is balanced toward the front, I now have more weight in the rear and the tail will drop? I have heard it discussed this way and the opposite, meaning someone has said if you move the CG forward that will make the plane nose heavy, and that makes no sense to me. Can anyone explain this to me? Thanks a lot.