Digital calipers use a silver oxide button cell, typically the SR44 size, aka 357, 11.6mm diameter by 5.4mm high. A genuine SR44 or 357 cell is hard to find, and the alkaline LR44, which is the same size button, and same nominal voltage, is very common and easy to find. This alkaline LR44 cell is put into toys, laser pointers, etc., and has gotten very cheap because of the large quantities made in China. However, alkaline buttons have much less mAh capacity, and have a critical weakness when used in devices like digital calipers that quit working when battery voltage falls. Alkaline cells quickly "droop" their voltage (they have a non-flat discharge curve), compared to silver oxide, and thus don't run calipers for very long before the display fades or blinks from low voltage.
TLDR: SR44 lasts longer but rarer + more expensive. Difference due to constituent materials. Otherwise geometry and purpose is the same.
source: http://www.truetex.com/buttons.htm
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