All Model S and X currently use 18650 cells. All 2170 production is going into the Model 3. The S/X pack groups the cells into modules. The small pack cars (60, 70, and 75) use 14 modules, and the large pack cars use 16 modules. There have been 2 generations of 18650 cells and 3 generations of module design.
Below is my breakdown of the pack and cell generations to date. The highlighted blue section is the small pack data and the highlighted green section is the large pack. It's unconfirmed, but Tesla may have changed the chemistry when they came out with the 100 KWH pack. Jason Hughes did a breakdown of a 100 pack and the numbers in the last column come from his data. To get his numbers would require a slightly denser chemistry than the 90/75 packs had.
As you can see, when they went from the 70 pack to the 75 pack it was to standardize modules between the two packs. The 70 and 60 packs had fewer cells per module, but the 75 had/has the same pack as the 90. Standardizing on the same module for both battery packs saves them money and it's inevitable they will do it eventually if they haven't already done it.
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Currently 18650 cells are made in Asia and the 2170s are made in Nevada. Jason Hughes has said there is enough height in the existing modules to squeeze in the extra height of the 2170s. It shouldn't require a chassis redesign.
When the Model S was designed, they went with 18650 because they were widely available. It was a cell frequently used in laptop batteries. However, at that time they figured out what the optimum form factor would be to trade off energy density and cooling ability and they came up with the 2170 size. I believe they designed the car to accept a redesigned pack with 2170s at some point because their long term plan was to use them.