Parkwood is not part of the Villages. They are separate development just like Lakeside Landing. However, if you lived right next door at Bison Valley, a Villages development, or off 301 at Oxford Oaks or off 466 at Spring Arbor you still wouldn't be able to use the facilities even though they are Villages developments. In fact I believe you couldn't even get a guest pass to use the golf courses because you would be living in Sumter, Lake or Marion County, unless you were part of the immediate family of a Villages resides. If someone has better info, you can correct me.
If you're trying to find a cheaper place to find new housing, I would suggest Lakeside Landing off Rainey Trail. It's not part of TV, but you would only be one mile from LSL and could visit the squares, the movie theater, the restaurants, but could not play golf, softball, pickleball or the rec center.