Scale refers to how two or more objects relate to on another in a room based on the actual, relative, and visual weight or size. There is physically small and large scale and there is visually heavy and light scale.
Proportion refers to how one part of an object relates to other parts of the same object and the object as a whole. Furnishings, while being in scale with the room, must also be in proportion to one another.
Scale refers to overall size and proportion refers to relative size. Scale and proportion principles help the viewer organize an image and they can be used to create or minimize points of emphasis.
Symmetry is an imprecise sense of harmonious or aesthetically pleasing proportion and balance. Symmetry is mirrored on either side.
Asymmetry is the absence of symmetry. It is an unbalanced distribution of objects in a room. Creating a sense of balance using different objects but at the same sizes are not quite the same.
Symmetry and Asymmetry are the same by each principle create a sense of balance. Although symmetry uses mirrored objects and asymmetry uses different objects.