There are different types of firewood logs with different burning characteristics. The biggest differences between wet an dry will be the differences between species. The main burning differences between species will be determined by the density of the wood. Generally the heavier or more dense the wood is the more heat it will have and the longer it will burn.
Hardwoods are usually, but not always, more dense and have more total heat than softwoods. Because of this, hardwoods are usually more popular for heating with wood stoves and usually cost more than softwoods. Dense hardwoods usually burn hot and for a longer period than softwoods but can be more difficult to ignite.
Softwoods and low density hardwoods usually ignite easy and burn with more intense flames but burn faster and have less heat energy than dense wood. This makes softwood good for starting fires and getting quick heat. It is also good for campfires and open fireplaces where you want nice flames and the atmosphere they create.
There are also different types of firewood logs that will produce more ash than others. With many types of wood much of the ash will come from the bark. Wood with thick bark will often produce more ash than pieces with thin or no bark.
For cooking, hardwoods are usually the more popular types of firewood logs. Most softwoods are resinous and the resins can produce smoke that will leave flavors on your food that can taste bad and may not be the most healthy to eat. Although there are exceptions. Hardwoods not only make food taste better, it also produces coals that produce more steady radiant heat.
There are also differences between types of firewood logs and how they split. This can vary greatly between species and even individual trees. Straight grained wood will usually split easier than twisted or stringy grained wood.
The types of firewood that are best for burning all depend on what you want from the wood and your own preferences. All wood will burn if it is dry but some are better suited for different needs.