The key words here are prop planes, turboplanes, and light jets. Prop planes like the Cessna Caravan are popular because they're roomy (the seats are like business class, and often configured face to face). More popular these days are planes like the six- to eight-seater Pilatus PC-12, and KingAirs, which fly faster and feel more like jets. And then you get into light jets like Learjets, Embraer Phenom 300s, and Citation CJ3s, and Hawkers, all of which are sleeker and more streamlined, and can fly for four to five hours, for slightly longer trips.
On a Charter Flight, passengers aren’t limited to on of 2 or 3 entrees being served. They can literally design their own meal or order from a restaurant of their choice to be enjoyed while traveling in supreme comfort. There is also a wide variety of entertainment options on a charter flight. Many aircraft used for charter flights have free WiFi, high end sound or entertainment systems with iPhone/Android hook-ups and even satellite TV.
One particular type of operating lease is the wet lease, in which the aircraft is leased together with its crew. Such leases are generally on a short-term basis to cover bursts in demand, such as the Hajj pilgrimage. Unlike a charter flight, a wet-leased aircraft operates as part of the leasing carrier's fleet and with that carrier's airline code, although it often retains the livery of its owner.
Though the early Lockheed Jetstar had four, most production business jets have two jet engines, mostly rear-mounted podded engine. If mounted below their low wing, it wouldn't allow sufficient engine clearance without a too long landing gear. The HondaJet is the exception with its over the wing engine pods. Dassault Falcon still builds three-engine models derived from the Falcon 50, and the very light jet market has seen several single-engine design concepts and the introduction of the Cirrus Vision SF50 in 2016.