"Power symbol" and "power object" are not only not interchangeable, they are also non-identical.

"Power symbol" is a term used in developmental psychology, particularly in reference to the adolescent stage. Examples of power symbols are guns, cars, and action hero figurines.

"Power object" is a term used in magic, and it most probably originated with the North American Indians' use of power bundles and medicine bundles. Examples of power objects are implements such as talismans, amulets, and wands.