Capital costs are costs for typically physical things that are needed to run the business. For example, a factory or a machine. Thus, capital costs are typically investments.

Operating costs are the costs to operate the business for things like supplies and wages.

For example, if you were to open a popcorn stand, capital costs would include the stand, the popcorn maker and the cash register. Operating costs would include the popcorn kernels, paper for the cash register, and electricity.