In cost accounting, ou can either use "actual" cost or accounting standard called Standard Costing, where you establish "standard" costs for certain items, and then on a company or product level analyze your variances of total cost versus the "standard cost" you have been applying.  So "Unit Cost" is the amount you have determined is the most accurate cost on a "unit basis" for that Standard Item.  It should logically follow then that "Unit Price" is the price you bill your customer for that Standard Item.  The "Unit of Measure" refers to the definition of a "unit" (square foot, linear foot, ounce, pound, etc.).

Art Minds
Senior Independent Consultant