^JB^ -- Both horticulture and horticulturists are very good words and your use was correct for your grandparents.
Saying that they are gardeners is more casual. Of course, someone might then ask... Hmmm, what do they grow? And then you could say, "Why, they grow ornamentals."
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You could get a good conversation going with that gambit.
I would be interested in the ornamentals they grow. Anything like this??
My confusion was that the garden you showed us looked (to me) like a home vegetable garden. But, now I think it is what I would call a "market garden." Those vegetables are to be sold and could be considered as agriculture, just as you said, although we could still say that those gardeners were horticulturists too... but hoping to make some extra cash.
Here is an "allotment" garden in England. I think these can be leased from the local council both for home use (horticulture) or for market produce.