I am changing the shifter cable on a bike with grip shift. I heard the cable casing is different than other types. Is the cable different?
This is a slightly fringe topic that will draw some blank stares at many cable-selling establishments.
Common shift cables come in 1.2mm and 1.1mm thicknesses for the cable part. SRAM (and I believe Sachs before them) specs 1.1mm for all Gripshift models. Shimano and most other companies use 1.2mm.
The difference of course is tiny. It's negligible in most cases, and a lot of people aren't aware it even exists. Nevertheless, the notion is out there that SRAM Gripshift can have issues with binding or excess friction due to internal clearances if a 1.2mm is used. Personally I haven't experimented much with using the technically wrong thing so I won't speak to how much difference it actually makes and when.
Many third party cables are 1.1mm for maximum compatibility, but not all. There are no disadvantages to using a 1.1mm in a Shimano shifter. Also Shimano Revoshifts, sometimes colloquially called Gripshifts, use 1.2mm without issue, like all Shimano shifters.
If you want to keep it simple just buy any uncoated SRAM cable (I just noticed they list their coated ones as 1.2mm). Many brands won't say whether they're 1.1mm or 1.2mm on the package. But it's very likely a marginal difference if any regardless. Gripshift is the only context where I've ever heard talk of it mattering.
Shift housing manufacturers do not typically list any compatibility distinction between 1.1mm and 1.2mm cables.