Newtown was incorporated in 1711. It brought together, five towns, Hatterville, Dodgingtown, Sandy Hook, Botsford, and Hawleyville. In my post about the Sandy Hook elementary school, I explained that Sandy Hook was but a SECTION of Newtown and NOT a separate town.
Re your picture...yes, that's how signs are and the next sign, for Exit 9, says Brookfiled, which is the next town over and Newtown, but takes you to the Dodgingtown. There are also smaller areas, within Newtown, that have their own names; however, it's usually just the 5 major towns that are talked about as separately named places.