Acetylaldehyde is definitely the harshest substance resulting from alcohol consumption and is probably the bulk of the hangover.
One of the other leading theories on why repeatedly distilled spirits leave you (albeit slightly) less hungover is the removal of fusel alcohols (carbon>2). Different fermentation processes will spout off different compositions but they are typically going to be removed using multiple distillations.
Worth noting that most of these fusel alcohols are actually extremely common in cannabis and will show up in a lot of cannabis terpenes. They’re known to have intoxicating effects.
Most of them smell a bit unpleasant and will give you an immediate urge to cough if you smell them too closely so it would make sense to me that they’d contribute to a headache when consumed in liquor. Most of them smell like a mix of petroleum and rotten bananas/cantaloupe but lend well to more complex aromas.