What are the differences between the CH-46 and the CH-47?
Why does the military run both instead of settling on one?
The difference is in mission, and the difference is non trivial.
The twin rotor configuration goes back to the 1960's. ("Flying banana" Piasecki H-21. The CH-47 replaced it in Viet Nam in 1965). Chinook became the Army's heavy tactical lift during Vietnam. Like the C-130, that particular design is timeless. The CH-47F is the current configuration. It carries about twice as much as a CH-46 could. It is also one of the faster helicopters there is (it can fly almost 200kts) though the CH-53E has flown faster.
The CH-46 was an adaptation of the same idea, but made smaller and marinized: it had to meet a host of Marine Corps and Navy requirements to fit on amphibious ships and supply ships. Space and fit are non-trivial limitations when writing requirements for naval aircraft. (As an aside, the US military no longer operates the CH-46. It appears that the last CH-46 squadron in the USMC, HMM 774, let go of its last Phrogs in 2015 and is now VMM 774, flying V-22's. The Navy Sundown for CH-46 was in 2004.)
Not having to take off some power for a tail rotor is an advantage. The CH-46 mission for the Marine Corps was vertical assault (it carried more than a Huey and predecessors like the CH-34); for the Navy, it was the VERTREP mission.
The payload and maneuvering benefits from the lack of a tail rotor made the VERTREP mission a perfect fit for the CH-46. One of the challenges in ship borne operations is the ability to run simultaneously resupply by air and ship-to-ship (UNREP) while not being operationally constrained (for the ship drivers) "getting into the wind." That limitation tail rotor helicopters don't handle as well as the CH-46. (That point was a core argument against CH-60S as replacement for CH-46; but that's another matter). I've flown VERTREP in helicopters with tail rotors; the CH-46 was less constrained than we were.
What about Marine and Navy Heavy Lift missions?
The Marine Heavy lift (analogue to the CH-47 for the Army and Air Force CSAR) is fulfilled with the CH-53, and has been for over 40 years. The CH-53 can fold its tail to fit on a ship. Even with folded blades, the Chinook's deck footprint is / was too large(at the time) on the amphibious ships in service. The Navy VOD (heavy lift) was handled by CH-53's for 40 years. They have since given that mission to the MH-53E minesweepers. (Flexible, that's helicopters!)
Smart Requirement Writing led to smart choices
"The Military" would have made a significant mistake "to just make one type" since back in the 60s and 70s, making mission specific aircraft was the way to go. Quite frankly, it makes for cheaper aircraft to build it for one core mission. (See the A-10 as a fine example of that).
Note: An early failure in "one size fits all" was the F-111. A current "one size fits all" example of cost going through the roof is F-35.
At the time the CH-46 and CH-47 were procured, the military was smart: apply the KISS principle to get aircraft that fit mission requirements. The Army and Navy mission requirements were not identical.
(So how do I know all that? 25 years Navy pilot (helicopters, ASW warfare specialty, did other stuff like Vertrep ...), significant experience in multi-service operations, and a few years having to work in an acquisition job.)
They are run by different services- the CH-46 was operated by USN and USMC (before their retirement in 2015), while CH-47 is operated by the US Army and other foreign operators.
Both the aircraft look similar as their genesis lies in the same program. During 1950, the Vertol company started work on a medium lift helicopter, which led to the development of V-107, which the US army ordered as V-107. However, they later changed their requirements (they decided to use Hueys for tactical transport instead of V-107), leading to the larger and heavier V-114. While V-111 entered US army service as CH-47A Chinook, the smaller V-107 entered USMC service as CH-46A Sea Knight.
Though they look similar, they are in fact, quite different. CH-47 is much larger, has more powerful engines and has a substantially larger MTOW (22t for CH-47F as against 11t for CH-46E). Practically speaking, the helicopters are similar only in their tandem rotor configuration- otherwise they belong to separate weight classes.
Unlike CH-46, production is still running for CH-47.Coming to visual differences, the engine placement, landing gear and side sponsons are all different in both aircraft. globalsecurity.org has some details on this:
Differences between CH 47 and CH 46; images from globalsecurity.org
Besides all the above differences which are correct, we can also add a type of difference the fate of them. Marines decided to retire and replace the CH-46 with the Bell/Boeing MV-22B Osprey whilst the Navy did the same with their UH-46 by MH-60S and civilian Pumas. The Army instead continue upgrading airframes as it has done since the 60s (upgrading A/B/C models to D, then D to F in the 90s) and nowadays is still fielding new build CH-47F-MYII blocks. This will assure the Chinnok a 100-year lifespan.