The words are close in meaning. Use "pertinent" for things that are directly applicable to the matter at hand. "Relevant" is a weaker connection. It merely means "related" or "connected". Here's an example to show the difference. Suppose police are investigating the cause of a car accident. The fact that the driver was using his cell phone when the accident occurred is both pertinent and relevant. The fact that he was wearing size 8 sneakers might be relevant but probably not pertinent. The police will write that down but will probably have no use for it.

Pertinent means related to a topic whereas relevant means having importance on a subject