They can mean the same thing. Something that is responsible or is a cause of something else. "Shoddy construction was a contributing/contributory factor in the collapse of the bridge." However, 'contributory' has a special usage. A contributory plan for a company is one (a health plan, for example) where both the employer and the worker contribute to the worker's health fund. 'Contributing' would not be used in such a case.

Contributing: verb (used with object) 1. to give (money, time, knowledge, assistance, etc.) to a common supply, fund, etc., as for charitable purposes. 2. to furnish (an original written work, drawing, etc.) for publication: to contribute stories to a magazine. Contributory: adjective 1. pertaining to or of the nature of contribution; contributing. 2. furnishing something toward a result: a contributory factor. 3. of, pertaining to, or constituting an insurance or pension plan the premiums of which are paid partly by an employer and partly by employees.