Slow barbecue (American): Slow cooking on the barbecue grill or on the spit rod (rotisserie) with the hood closed, keeping the temperature low to medium. Food is generally served well done.
Barbecue: Rather fast cooking on the barbecue grill at a high temperature. Steaks are usually cooked medium or rare.
Plancha barbecue: Quick cooking on a griddle, plancha plate or similar flattop surface. Temperature between 300 and 320ºC. Food is usually doused with marinades, alcohol, etc.
Teppanyaki cooking: Quick cooking on a griddle or similar flattop surface with temperatures between 150 and 170ºC. Vegetables are served crisp-tender.
PS: barbeque or BBQ is incorrect spelling. BBQ is a brand that managed to introduce their name so well that most people think that this is the way barbecue is actually spelled. A similar phenomena happened with the hoover, which really is the company name for a vacuum cleaner.