Hi Travis,
Copy Object is like a combo command. It offers quite a few workflows. When the output is set to the Surface or the Composite (option 1 and 2), the Associative checkbox is enabled. This is the "Adaptive" body workflow. Essentially, the body geometry from the source part can drive shape change in the target part within this particular assembly.
I personally prefer Surface output since it is more versatile in terms of modeling operations. Composite is a group of mixed bodies (surfaces and solids). It is more for representing the source part, not for modeling operation purpose.
The option 3 and 4 are both non-associative solid outputs. The difference is that #3 just copies the solid body from its position in the assembly to the target part. There is no link established between the target part and the source part. The #4 option does the same but places the copied body to Repair Environment (a persistent, non-feature-based, and non-parametric environment to fix imported body geometry), since Copy Object command can also copy solid bodies within the target part itself, not just across the part.
I notice you have quite extensive Fusion experience. The major difference between Fusion and Inventor is that Fusion tends to manage all component definitions within one design, while Inventor manages individual parts and assemblies as files. Each component can stand on its own or be referenced in another component. There is distinct boundary between two components (two files).
Many thanks!
Johnson Shiue (johnson.shiue@autodesk.com)
Software Test Engineer