The following is a list of terms, and the way I use them or what I feel they best represent. Different people have different takes on many of the words. For many of them, I don't think there is necessarily 1 correct definition.
BBQ Bar-B-Q Bar-B-Que - Most people seem to think bbq means slathering a thick sweet sauce on food. I think good bbq doesn't even need a sauce. Some people think it means that food has to be cooked "slow and slow." Personally I think bbq might be better left as a philosophy. Consider it more about the gathering of friends and family than some nitpick points about the cooking gear, fuel, etc.
Grilling - Most people are familiar with grilling as their classic form of backyard cooking. Put a wire grate over a bed of hot coals and cook your food directly above it. Grilling is usually at higher temperatures.
Smoking - Smoking refers to flavoring foods by exposing them to the smoke of burning hardwoods chips, chunks, powder, or pellets. The smoking process can be hot or cold. Most people will think of hickory or mequite, but apple, cherry, pecan, oak, alder, peach, and a variety of other woods are often used too.
Direct Heat - See grilling. Food is cooked directly over the coals. Sometimes direct cooking techniques rely on flavor from smoke woods.
Indirect Heat - Food is not cooked directly over the coals. Often the coals are pushed to the opposite side of the grill and cooking is done with the lid on, or the coals may be seperated from the food by a water pan or some other heat dispersal device. Traditionally indirect heat is used to make slowed cooked bbq dishes like pulled pork, ribs, and brisket. Today, many people cook with indirect heat at higher temperatures than the traditional 225-250F range, leading to argument over if they should be called bbq or not. Indirect heat often relies on smoke wood flavor. Direct heat is great for long slow cooks.
Smoke ring - People often panic when they cut into their meat and see pink on the edges. This is normal for smoked meat. The nitrogen dioxide in the smoke is absorbed as nitrous acide on the meat and is drawn in and reacts with the myoglobin in the meat to make a pink ring. Myoglobin is the stuff that gives muscle color. The same effect is seen with cured meats. Nitrates are the reason a corned beef or bacon has the color that it does. The ring does not impact flavor, although many like to use them for bragging rights. Expect to teach guests and remind them that if meat the meat is cooked on the inside, the outside cannot be undercooked. Thinner meats, like pork ribs, might be thoroughly cooked but also pink throughout. The smoke ring stops forming somewhere between 140F and 160F, but smoke flavor is continually deposited on the meat. Briquettes produce more nitrogen dioxide than lump. A briquettes or two in with the lump or on a woodchip pan can help. Moist meat will also take on a better ring. You can even "cheat" and sprinkle some Morton's Tenderquick on your meat and let it sit for 10 minutes before rinsing off to add a faux ring.
Pit - Common reference to the cooking appliance used for indirect cooking.
Rub - A mix of spices applied to the meat either minutes or hours before cooking. Bbq rubs usually rely heavily on salt, sugar, paprika, and chili powders.
Brine - A heavily salted water that uses osmotic action to moisturize meat. Usually includes sugars and additional flavors.
Injection - Any liquid injected in the meat either the night before or the day of cooking. For pork often includes apple juice, water, sugar, and salt. Beef injections can include things like beef stock.
Marinade - A solution that food soaks in for several hours to overnight to take on flavor and moisture. An acidic component helps tenderize tougher cuts of meat. Oil is often included.
Lump Charcoal - Hardwood that has been turned into charcoal. Nothing more than that. The pieces will vary in size, how they burn, and brands will show quality differences. Some may spark and pop a lot. Can burn very hot with unrestricted air flow, can be difficult to control temperature with, low ash production.
Charcoal briquettes - Charcoal that has been ground and pressed. Some contain additives that help them burn longer or more uniformly. Some people claim they can taste those additives, despite such charcoal being used to win bbq competitions. Briquettes burn very evenly and are easy to control, usually at the expense of being less capable of generating high heat and producing far more ash.