The sun emits two types of ultraviolet radiation that damage skin: UV-A, which causes premature wrinkles, and UV-B, which causes sunburn. Until about ten years ago, sunscreens protected against UV-B radiation but not against UV-A radiation.
Until about ten years ago, people who wore sunscreen were no less likely to have premature wrinkles than were people who spent the same amount of time in the sun without wearing sunscreen is best supported by the information above.