While Foxtel is a traditional pay TV service with a streaming spin-off (Foxtel Now), Binge is exclusively a streaming platform like Netflix. As such, they share a lot of the same content but there are exclusives reserved for Binge and some that can only be found on Foxtel.
Binge is a service dedicated to TV shows and movies and doesn't offer any of the news or sports channels offered by Foxtel. Unlike Foxtel, Binge doesn't have channels or "packages" so to speak, just three all-inclusive plan tiers. Unlike Foxtel Go, being a Foxtel customer doesn't automatically give you access to Binge. If you already pay for Foxtel, you'll have to pay extra to use Binge (or consider switching entirely.)