What type of battery goes into Casio G shock MTG900, Module 2638

CTL is the designation for a rechargeable secondary battery. The CR is a primary disposable battery and is a 3 volt cell. The CTL1616 while the same size as the CR1616 function completely differently and are not interchangeable. The CTL1616 is 2.3 volts and is recharged by solar or light or kinetic movement. The CR1616 is 3 volts is not rechargeable and will not function properly in a time piece designed for a 2.3 volt circuit. There is only one manufacturer of the CTL1616, Panasonic and they sell through Casio parts distribution.

CTL is stand for Cobalt Titanium Lithium Rechargeable Battery.
CR is Lithium Manganese Dioxide Battery.

The site shows the right one. To be 100% sure, you can take out original battery and read the writings- these will be exactly what you're looking for.
As these are 3 Volt Lithium batteries, they last quite a long time and I suggest that's why you thought they are rechargeable. Some of them can power up the watch up to 9 years (depending on watch movement).
When buying the new battery, do not mind the letters and manufacturers name- they may vary. Just make sure the brands name is familiar to you (SONY, CITIZEN, MAXELL, RENATA, CASIO, YAMAHA, etc) and the numbers are EXACTLY the same as on old battery, in this case 1616. Those numbers actually are the size of this particular battery: diameter 1.6 cm X height (thickness) 1.6 mm.
So, if you will get the wrong numbers, your battery will not fit in to the watch simply by size.
I hope this solves your question.

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