Charcoal is made by burning wood in a low oxygen environment, driving off water and organics, while carbonizing lignin, cellulose, etc. Coal is a petrochemical mass formed underground from organic matter over long timescales.
Fresh wood contains ~50% water (up to 70% for certain species), 'dry' wood lies around 15% water. Depending on the type of gasifier you can feed it anything between fresh from the tree to kiln-dried wood. Starting a gasifier requires dry wood or charcoal but once it is going it will do a lot of the drying itself. The reduction process in the lower part of the hearth - where the gas production goes on, reducing CO2 to CO - can also reduce H2O to H2. The end product of a wetter wood will be gas with a higher H2 content next to the CO which forms the main combustible component in wood gas. Yes, wood gas is mainly carbon monoxide and as such highly poisonous, you do not want to start a gasifier in an enclosed environment nor open an unvented gasfier in such.
Dried wood suitable for burning is around 20% water at most, else it won't burn with much heat. It can go down to around 6% IIRC for kiln-dried wood suitable for construction.