Word Choice – When to Say ‘Woods’ and When to Say ‘Forest’

To add more nuance (and confirm what's already been said) to the difference, I find (in AmE):

• you can say 'a forest' (in general), or 'the forest' (a particular one), and 'the woods' (the one that you're walking through), but it would seem strange to refer to an collection of trees as 'a woods' (because of number agreement) or 'a wood' (because that would refer to a particular piece of lumber.
• 'forests' are bigger than 'woods'. But a small collection of trees is not necessarily 'the woods'. Something smaller (without specifying actual size) would be called 'a stand of trees'. (i.e. if you can go into the collection and not see the end of the trees, then you're not in a stand of trees)
• 'forest' has a slightly more official, formal feel to it than 'woods'.