In reply to Bobby B.

PayPal connect's to Visa/MC via it's acquiring relationship with Chase Paymentech. Paymentech is PayPal's processor and PayPal is a Payment Service Provider acting as a Merchant Of Record for the entities it underwrites. PayPal is not a processor.

A Processor connects directly to the card association rails and can send settlement messages to Visa/MC. A gateway does not connect directly to Visa/MC and instead (as you pointed out) routes messages to the processor.