I *like* both terms, botanical perfumery sounds nice but as someone mentioned it doesn't always mean all natural just no animal, might be better to say natural botanical.
Natural is what I'm used to using and I use animal stuff like beeswax, honey, propolis and africa stone tincture (which is basically tinctured poop) and I ambergris, sort of like a person that only eats natural foods and likes their bit of wild salmon and sea trout too.
I often think when I here the term natural perfumer that it implies that maybe they were born that way...a natural perfumer ....
I sort of liken it to the difference between only using natural sounds to make a song as opposed to using electronic or a mix of both.

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