Looks like a decent smoker there, lots of potential. The answer to your question is maybe.
HA! Just teasing, welcome to SMF!
What i mean is, yes it can be considered a wood smoker, and yes it could also be considered a charcoal smoker, it's up to you and how you want to use it. Depending on what you are cooking, and what temps it should be cooked at - PLUS, the amount of "wood flavored" effect you want - you can do all wood, all charcoal, or a mixture of the two!
Here is my take on it - and this is based only on what i can see in that one picture:
The far right firebox, CAN be grilled in - on that top rack you mentioned. For instance, you could do an awesome ribeye over a 500° wood and charcoal mix!
You could also grill in that center section, or "Smoking/BBQ chamber", but in my humble opinion, that's not what these rigs are really made for. You should use that center chamber like a true 'horizontal offset smoker'
. That's where you'll do ribs, pulled pork, brisket, etc...all the good stuff!
That's because the heat in that section will be optimal for smoking meat - not grilling - when you have a fire in the firebox, but NO fuel in the smoking chamber....you are doing true, indirect cooking.
This is just my opinion, meaning - yes it's possible to grill in the center chamber, but you might as well get a Webber Kettle if you are going to grill a lot. To really use your new smoker to it's potential, you want to keep ash OUT of that center chamber - and use that for SMOKING MEAT only.
For example, brisket or pulled pork. They can take a lot of GOOD smoke. (we call it thin blue, not white and billowing!) Even with a lot of good smoke, they turn out tasty and tender. So in that instance, you could burn more wood that day and cook in the center chamber with the fire in the firebox only. The next day, you could burn charcoal with a few wood chips every so often and smoke salmon in the far, upright chamber!
That far left, tallest upright chamber is what many of us refer to as the "cold smoke" chamber, or "warming section", "slow smoke", etc...in there you can do fish, cheese, and many other things that are smoked at lower temps!
You get the idea - it's logical that the farther away you go from the fire source, the lower the temps are. Sooo...the magic formula is learning the proper techniques for smoking different foods.
Just use this forum and search the "charcoal" smoker section AND the "wood burning smoker" section - read enough here and you'll learn plenty.
Also, Google terms like "offset smoker with warming box"
and you'll learn even more, from all different sites.
Of course, this is still the best, authoritative source on all things involving the love of smoked meat!
The bottom line is, you just have to read a ton about what you want to smoke, and what fuel to use, and what temps to cook at
- and you're in the game!