A service marketplace is an umbrella term for any kind of marketplace where services are offered and bought. Examples of service marketplaces include Booking.com, Upwork, and VRBO.
A peer-to-peer, or consumer-to-consumer, marketplace, is a type of service or product marketplace. Here, individuals connect to offer and buy products or services from each other, and the pricing depends entirely on the seller, as opposed to on a company or startup. Think: Depop, AirBnB, and Etsy.