Yeah it's very similar, I guess the difference is where you're starting from.

Wood contains the carbon/charcoal as well as volatile & flammable gases that are released with heat. After a period of burning, your wood turns to charcoal.

When you start with charcoal, you start with just the amount of charcoal you need & it burns in an easily controllable way with O2 control. Heat regulation is a little easier.

Wood is a little more random & you rarely have just pure charcoal. Ideally you have a good bed of hot smouldering charcoal to cook on. In reality, you are pressured for time (hungry peeps wanting meat).

In summary, using wood tends to result in a hotter grill with more smoke flavour. You'll tend to have a good dark crust but a rarer peice of meat from the higher heat.