Primarily, the differences come down to which characters are being featured in each book/sub-team.
When you think of The Avengers, this is the comic - and team that should come to mind. Any and all members are likely to show up.
This is a brand new book which Marvel describes as
"The premise of the book is that it's the Avengers, doing big things, because it's an Avengers World now," editor Tom Brevoort explains. "But while we'll field the same potential lineup of 18+ Avengers in WORLD, we'll specifically be looking to give greater screen time to some of the newer Avengers, like Hyperion, Smasher, Cannonball, Shang-Chi, Starbrand and Sunspot."
A very recent book, this book features the android members of the team. Marvel describes it as
When a brave new world is unleashed, only one team of Earth's Mightiest Heroes can save us from the future -- AVENGERS A.I.! THE VISION! HANK PYM! VICTOR MANCHA! DOOMBOT! The mysterious ALEXIS! MONICA CHANG, AGENT OF S.H.I.E.L.D.!
This book has not launched yet, but it is a sequel to Avengers Arena. It will feature Hazmat, Bloodstone, Death Locket, Cammi and Anachronism. Marvel describes it as
Thrust into the kill-or-be-killed environment of Murder World, only a handful of young heroes escape the confines of AVENGERS ARENA. Those hardened survivors find themselves behind enemy lines, infiltrating the Masters of Evil organization in AVENGERS UNDERCOVER.
Can kids like Hazmat, Bloodstone, Death Locket, Cammi and Anachronism hope to maintain their humanity in this clandestine operation? Does convincing their sinister new comrades that they’ve embraced their role as villains mean that they can never go back?
Murder World prepared them for death, but can they cope with living as Masters of Evil?
The New Avengers
The most recent volume features The Illuminati, who are all members of The Avengers.
Currently, this line up includes: Beast, Black Bolt, Black Panther, Doctor Strange, Iron Man, Mister Fantastic, and Namor the Sub-Mariner.
This is the "Black Ops" squad of The Avengers. Since the Marvel Now! launch, SHIELD has taken over this group.
Currently, this line up includes: Maria Hill, Nick Fury Jr, Phil Coulson, Mockingbird, Taskmaster, Hulk, and Iron Patriot.
Known as the Avengers Unity Squad within the book itself, this team is made up of a mix of classic Avengers and X-Men members.
Currently, this line up includes Captain America, Havok, Rogue, Scarlet Witch, Thor, Wolverine, Sunfire, Wasp, and Wonder Man