Beginner Chef,
Basically, you have a BBQ cooker that apparently doubles as a charcoal grill (the smaller chamber on the left hand side, known as a firebox). Essentially, you can grill in the smoker box, or BBQ in the other chambers to the right. There is a difference, however, between BBQing and grilling.
Grilling is the act of cooking food on a grid over direct heat. Grilling lends itself to cuts of meat and fish that cook rather quickly, and are fairly thin, though there are exceptions. You wouldn't want, for example, to grill a chuck roast as the high heat (commercial grills are run at 700 degrees and up; home models less than that but still mighty hot) will coagulate the proteins so quickly that they will toughen or "seize," leaving you with very tough cut to try to eat. Steaks, fish steaks and whole fish, chicken parts (breast, thigh, etc.), lamb chops, pork chops and tenderloins cut into medallions all do well on a grill, as do vegetables and pizzas.
BBQing is a different matter. Essentially, it involves taking a relatively tough cut of meat (think brisket, ribs, pork shoulder and fresh hams, etc.), marinating in an acidic/salty marinade or dry rubbing it with a salty/sweet dry rub overnight, then cooking it "low and slow" in the cooker. What I mean by this is your fire goes in the firebox, and your items to be BBQ'd go in the cooking chambers. Temperatures are generally between 175 to 250 degrees, as the low heat helps break down the collagen in the meat into gelatin, making it tender. Higher temperatures to coagulate the proteins too fast, resulting in tough meat. And BBQing, real BBQing can take hours - the recipe I use for brisket is a 14 hour affair, but worth every minute.
As for cooking fuel, pellets, wood chunks, lump charcoal, wood logs and even propane can be used. Most home BBQers have access to charcoal, wood chunks and propane; some have access to logs (you don't have to keep restocking the firebox as often). Some use a mixture of charcoal and wood, others don't. I use wood when I BBQ as it delivers the smoke flavor we so love.
There are any number of books and online sources to guide you. Steven Raichlen's books are great, as are the ones by Chris Schlesinger. John Willingham wrote a great book which was my introduction to real BBQ, and I highly recommend it. Do a google search on BBQ, and you'll get thousands of hits.
Hope this helps,
Alan
