'occasionally' originates from Latin, specifically the word 'occasio,' where 'occas-' meant 'a happening' and '-ally' is an adverbial suffix. 'Dismiss' originates from Latin, specifically the word 'dimittere,' where 'dis-' meant 'apart' and 'mittere' meant 'send.'

'occasionally' changed from the Old French word 'occasional' and eventually became the modern English word 'occasionally.' 'Dismiss' transformed from the Old French word 'desmis' and eventually became the modern English word 'dismiss.'

Initially, 'occasionally' meant 'pertaining to an occasion,' but over time it evolved into its current meaning of 'sometimes.' 'Dismiss' initially meant 'to send away,' and this meaning has largely remained the same in modern usage.