Very simply.. alchemy was mainly founded on the idea of transmuting metals (especially into gold) and finding/making the philosphers stone. The alchemists had very little understanding of the underlying reactions and concepts to what they were trying to do.
Chemistry is a more evolved verion of this in which the underlying principals are (mostly) understood and experimentation is more analytical rather than the alchemical approach of mix-> burn -> see if it worked.
This is extremely simplified the evolution/change was far more complex
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