Buick and the CVT . . .
There is a reason Buick went their own way with automatic transmissions for so many years. Back in the '30s many attempts were made to provide some form of automation for shifting using a variety of methods: vacuum shift assists, pre-selectors where one selected the next gear using a tiny lever and the gearbox would then change to it when the clutch was pushed, etc. At GM Cadillac and Oldsmobile were the lead divisions for what became the Hydramatic. GM had pioneered the synchronized manual transmission starting in the late '20s but saw the need to move beyond that. As a part of this program experiments were going on with both automatic shifting planetary transmissions and fluid couplings. The Ford Model T had used a manual planetary transmission with two speeds controlled by a foot pedal so all the engineers would have been familiar with the concept; one of the advantages of a planetary gearbox is that it can be shifted under load without a separate clutch. Fluid couplings were also being studied, these allow a car to remain in gear and idling at a full stop and also can smooth out rough shifts. Daimler in England used fluid couplings (they called it the "fluid flywheel") with their manual transmissions for many years in the pre-war era as the coupling made it very easy to drive smoothly, a nice feature on the large luxury cars they specialized in. The first GM automatic was introduced by Olds in '37 using the automatic planetary gearbox but a conventional clutch, which meant the driver still had to de-clutch to stop, and the shifts could be rough. For the first Hydramatic they combined the fluid coupling with the planetary gearbox, which allowed the elimination of the clutch pedal and gave very smooth shifts. It was the first successful true automatic transmission, introduced for the 1940 model year.
Buick had a program of its' own in the thirties to develop a CVT, or continuously variable transmission that would seamlessly shift from a low ratio to a high ratio. They were using a toric drive system, basically like two dinner plates held at right angles to one another. One plate was hooked the engine, the other to the drive wheels. By varying the relative position of the plates the gear ratio could be seamlessly changed; there was no actual shifting of gears. The concept was brilliant, but they couldn't find friction materials robust enough to make the system reliable and durable. Once it became obvious that the Hydramatic was both reliable and durable GM management ordered Buick to stop spending money on the toric CVT. For a very short while right before WWII Buick therefore offered the Hydramatic, though this was after Olds did so.
An important part of this situation is that while Oldsmobile and Cadillac frequently worked together on projects, Buick saw them both as enemies. Buick fit into the narrow band between Olds and Cadillac, and a well optioned TOL Buick was often more money than a lower end Cadillac. Even the King of England, Edward VIII, had a Buick - that was the car he and "Mrs. Simpson" used when they left England for France immediately after he abdicated the throne to marry her. Technically, that car was a Canadian built Buick and thus a product of the British Empire. Buick also had a loyal customer base who could have afforded Cadillacs but felt them too flashy. As a result of their reputation Buick did not like to be seen following in the footsteps of Olds and Cadillac, not one little bit.
During and right after WWII Buick's transmission department was busy creating a new automatic that had to have three virtues: it had to be very, very smooth and thus more luxurious than Hydramatic, it had to be reliable, and it had to have no connection with the Hydramatic Division of GM. Their solution was to use a very simple two speed planetary gearbox that did not shift for itself combined with a fairly sophisticated torque converter, which is itself a more advanced form of fluid coupling. In operation it was the opposite of Hydramatic: Hydramatic relied on four gears to provide the right ratio for conditions and the fluid coupling did little other than add some smoothness and let the car sit still while idling, while Dynaflow didn't shift gears at all during normal operation but relied on the torque converter to vary the theoretical gear ratio. Thus the Dynaflow was a sort of CVT, since gears didn't shift there were no shifts to be felt. In practice it worked well enough, certainly the smoothest automatic on the market. However, it was very inefficient which caused big Buicks to generally be considered inferior at acceleration to Oldsmobiles or Cadillacs. Buick refined and significantly improved the Dynaflow through the early '60s, but like the toric drive CVT it was ultimately a dead end. When GM introduced the Turbo-Hydramatic Buick finally gave up on Dynaflow, but in compensation the Turbo-Hydramatic did have a torque converter instead of the old fluid coupling, and some versions clearly took advantage of Buick's expertise in torque converters. Buick did however refuse to use any form of the name "Hydramatic" for many years and took to calling all of their automatics "Super Turbine" followed by a number.
Chevy also did their own thing with automatics, in their case they wanted something cheaper than the Hydramatic. Introduced in '50, that was the two-speed Powerglide. It was cheap and reliable, although by the late '50s Chevy felt the need for something more sophisticated for their upper line models. They solved that problem with the Turboglide, their version of the Flight-Pitch Dynaflow. Most Chevy customers preferred the Powerglide as it was much cheaper, and many of the cars that were equipped with Turboglide were converted to Powerglide if the Turboglide ever failed as it was expensive to repair. For these reasons, very few Turboglides exist today.