Hello! Basically, what defines a charter airline is that all seats on their aircraft are sold to tour operators. Charter airlines are not allowed to sell their own seats (in the U.K. anyway), all seats are sold through tour operators. Usually this is for 7 or 14 day holidays. You book the holiday including the flights. You can book seat only on these flights, even from the airline's own website, but you are still booking with a tour operator. That's the difference. Yes they operate a regular 'scheduled' service, but its all in who markets the seats.
It all came about in the 60s/70s when such tour operators began providing affordable holidays to the public at large. Scheduled operators were too expensive and often didn't even fly to the required destinations. Therefore the charter airline was born, specifically to take these passengers. This is why we see infrequent schedules, i.e. Uk-Tenerife mainly Tuesdays and Fridays.
In recent years, with the loco boom things have started to change. Tour operators and associated charter airlines have seen their market eaten away at bit by bit. They have adapted in many ways, some have set up their own lo-cost airline, all have started selling flexible seat onlys, and First Choice have even kitted their long haul aircraft to better spec than BA
As to why you don't have so many in the States? Probably because the way you holiday is very different, you don't really need to go abroad, you can get a scheduled flight reasonably competitive to pretty much anywhere, therefore no need for the charter airline.
Hope this helps, think I've covered most bases!