It could also be a British thing. I don't recall any Americans referring to a wooded place of set boundaries as a "Wood." Maybe they do in some regions, but not in any that comes to mind. Even as a proper noun, it's "Woods" in every case I can think of ("Pattersons Woods," "Wickersham's Woods," etc.)
Robert Frost "The Road Not Taken" begins with the lines "Two roads diverged in a yellow wood, And sorry I could not travel both
And be one traveler, long I stood . . ." and ends:
"I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference."
Wrt British writers vs American writers, I see the use of "woods" pretty evenly split between the two so I don't really think that's it. Could be; I just don't see it.
When dictionaries show that two or more words have the same meaning and indicate they're interchangeable, it comes down to contextual imagery and a sort of texture differentiation (or distinctness) between the words. That contextual imagery and textural word choice helps to set the mood and tone of the story and can elevate your text.