There are two objects in this image. There is a square and a cylinder (that's been boolean'd into pieces.) What I want is to merge these two objects. I know about ^J, the merge option under Mesh, and about boolean union. What I don't know is which of these will join the meshes together do that there is literally no gap between the cylinder and square. I get the idea that join makes many objects into one. But I see nothing that shows the meshes are merged. Same thing for union. What I am looking for is one solid object. Does this make sense?

There are two objects in this image. There is a square and a cylinder (that's been boolean'd into pieces.) What I want is to merge these two objects. I know about ^J, the merge option under Mesh, and about boolean union. What I don't know is which of these will join the meshes together so that there is literally no gap between the cylinder and square. I get the idea that join makes many objects into one. But I see nothing that shows the meshes are merged. Same thing for union. What I am looking for is one solid object. Does this make sense?