The smoke is burned particles of whatever is burning. So a forest fire produces smoke in the form of sot. This may have some effect on aircraft engines as the carbon can build up in a few places. However nothing major. Volcanic ash however is quite different as it is made up of tiny pieces of rock that have been molten and cooled down to glass. And where sot from forest fires will burn when heated the glass from a volcano will just melt and clump together in large pieces of rock inside the engine.
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