We say "Can't see the forest for the trees". I use both "wood" and "woods", if I use the word at all.
When I think about how I think about groups of trees, I would think of a "wood" or a "woods" as fairly small - say 100 acres. A forest is bigger and older, and wilder. Here in Northern Ontario we refer to "the bush". So I live on 160 acres, mostly bush, with about 10 acres cleared. The bush is made up of conifers and deciduous trees (and tamarack, which is both a conifer and deciduous). The trees are quite large, and the undergrowth tangly, although this is not a requirement!
The phrase "sugar bush" refers to a stand of sugar maples which are tapped for syrup in the spring (which we are doing right now). It's never a "sugar wood" or "sugar woods" or "sugar forest".