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The Cayenne pepper. is a bit milder, rating at 30,000 to 50,000 Scoville units. They're named after the French Guiana city of Cayenne. I'm sure you're familiar with the Cayenne pepper; it's ground and sold as a pretty common spice.
They're from slightly different plants. Cayenne pepper is from the red hot chili pepper, also known as the bird pepper (Capsicum annuum). Peri peri is from the bird's eye chili (Capsicum chinense). Peri peri sauce (and some peri powders) also contain extra ingredients, such as citrus peel and tarragon. Thanks!