There's charter flying. You work for a company that has a Part 135 operating certificate. Other companies and individuals charter aircraft with you. Basicly they pay for the airplane by the hour. Most aircraft used in charter will be leased back from owners who want charter revenue to offset their costs.
Then there are fractional operations. You work for a company that sells shares of airplanes to companies and individuals. These share owners get a specified number of hours in an aircraft type. Fractionals also usually have an inter-change program where you can upgrade or downgrade for a particular flight based on your needs for that flight. This type of flying is done under Part 91 Subpart K and sometimes Part 135.
There's also opportunities to fly an airplane (or fleet of planes) for a company or individual. These jobs can be very good or very bad, depending on who you work for. You could fly a Cessna 172, a Boeing Business Jet, or anything in between. You could fly a single airplane or airplane type or you could fly two or three different types. The really good jobs are rarely posted to the public. You learn about most of them from networking.
In the hangar I work in, there are five other flight departments. One is home every night and typically only works Tues-Weds-Thurs. In the last 15 years or so, they've flown once on a Saturday and never on a Sunday. There's also a flight department that flys about 6 days a month per pilot and they're never in the offie. There's also a flight department that flys about the same amount, but their pilots have to be in the office 5 days a week even if they're not flying.
Do you have some specific questions?