That might be true in Latin but that isn't how English works. Botanic and botanical are synonyms, just like cyclic/cyclical, geologic/geological, mystic/mystica

That might be true in Latin but that isn't how English works. Botanic and botanical are synonyms, just like cyclic/cyclical, geologic/geological, mystic/mystical. Generally the -al versions are more common, but either one is fine.