Grilling meat does not make it BBQ. Let me explain this in greater detail: Grilling meat does not make it BBQ. There are 3 main types of grills:
gas...
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charcoal...
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and electric....
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Grilling is best used when cooking meat on a high direct heat. Thin cuts of meat work best for this form of cooking such as chicken breasts, steaks, and burgers. Grilling is not BBQing, it's called grilling. When is comes to your source of heat when grilling your meat...that's a personal decision and you will will be judged on that decision.
Electric = Lame. No picture necessary.
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Now for the part we've been waiting for. BBQing is the process of cooking your meat on an indirect heat low and slow (generally a more tough/thick piece of meat). The best source (and IMO only source) of indirect heat is smoking the meat using wood. You can use almost any wood to smoke but the most popular are Oak, Hickory, Mesquite, Pecan, Apple, Alder and Maple. All of these different types of wood have a unique flavor to them. Some pitmasters like to mix woods to mix flavors.
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<=== Some people like to smoke by putting a low heat charcoal and wood chips on one side of a kettle grill while the meat stays on the other side. This creates limitations such as space. (side note: water pan is used to help retain moisture)
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<===There are also those that smoke meat using what is called a "smoker". This creates an even heat and plenty of room for storage through different racks/layers.
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In the end, smoke is king. Smoking meats is what defines BBQ. It's the smell of charcoal/wood that cries BBQ, not a sweet molasses based sauce you throw on top of some dry flavorless meat. Don't get me wrong, grilling is legit for steaks, burgers, and chicken breasts. Lets not confuse grilled food with BBQ.