You will rank for both, once your site has earned enough authority on the topic. Google appears to be interpreting the terms as synonymous. You're likely seeing variations cause they (Google) are perpetually testing.
If I search for "woodscrews" today, only one page 1 search result (Screwfix) uses "woodscrews" in their title tag and on-page content. The nine others do NOT and yet still manage to rank on page 1 for the term.
You may see different results, but my point is, it may be less of a conundrum than you think. If you want to try to rank for both variations, you're going to have to out-optimize all competitors, including the 1 (Screwfix) that does manage to rank for a different spelling of the term. Screwfix has not used the spaced version of the term (wood screws) even once on the page. When you take into consideration EGOL's points, that may be a problem for you.
Also of note, Screwfix does NOT rank on page 1 for "wood screws" (with the space). So they really have traded off one for the other.