The terms barbecue and grill are definitely totally different things in my book but the two words have evolved to be synonymous (with the word barbecue being used when grill is what is meant) most likely because you barbecue on a grill. But yeah, barbecue means to slow cook over hours on the grill while grill means you slap the meat on the grill, flip it after a few minutes, and then a few minutes later, it's ready to eat.
You grill hot dogs, burgers, steaks. You barbecue brisket, ribs.
And when I say You, I mean, not me. I love good barbecue and grilled food but although I love to cook, I like to do my cooking indoors. Grilling is my husband's domain. Barbecuing is for people who really know what they are doing, and those people are few.
Back on topic, the grills pictured in the link posted by a PP is exactly what we have here. People go to the park, take the time to light the charcoal while the kids play, then grill lunch or dinner. It's an all day affair.