Ось що каже щодо forest, wood і woods кембріджський словник: http://dictionary.cambridge.org/dictionary/english/woods?q=Woods forest noun [ C or U ]
UK /ˈfɒr.ɪst/ US /ˈfɔːr.ɪst/
A2 a large area of land coveredwith trees and plants, usually larger than a wood, or the treesand plants themselves:
the Black Forest The children got lost in the forest.
wood noun (GROUP OF TREES) A2 [ C ] also woods [ plural ] an area of land covered with a thick growth of trees:
an oak wood
We went for a walk in the woods after lunch.
woods plural noun
US /wʊdz/ alsowood, /wʊd/
an area of land covered with a thick growth of trees:
Shaded from the sun, the woods were cool and quiet.
У першому визначенні сказано, що forest usually larger than a wood.