While it’s true that “it goes up in smoke”, not all of what people perceive as “smoke” from a chimney (or power plant stack, or car exhaust, etc.) is really smoke.
By weight, even well-seasoned and ‘dried’ firewood contains about 14–15% moisture when it’s left inside the house (where the ambient conditions will generally be >50% relative humidity even in a dry climate). So much of what seems to be smoke is actually steam. In that case, 14% of the “wood” weight is actually water.
The quantity of ash will be a factor of the type of wood and the heat of the combustion process. A well-oxygenated fire in a well-designed firebox will generally produce the least ash for the type of wood that is being burned, but not all wood species’ ash content is the same. And a lot of that ash escapes via the flue and the smoke. That’s flyash, as opposed to the “bottom ash”, the heavier ash particles that are left in the bottom of the combustion chamber.
Some of the escaping flue gas condenses on the walls of the flue in the form of creosote. Again, this is dependent upon the condition and dryness of the wood being burned, the species of wood, and the conditions of the combustion process and chamber.
The flue gas that escapes through the end of the flue (top of the chimney or smokestack), combined with the steam, is smoke; generally carbon dioxide, carbon monoxide, sulphur compounds (plus whatever else was in the wood), flyash (as noted above) and unburned particulate matter. Because the combustion process is not 100% efficient.