I guess it means there is no lag between the time when you press the shutter release and the time the photo is saved

I may be wrong, but higher end PnS and DSLR shouldn't have that problem at all, provided appropriate accessories e.g. Flash cards are used

from what i know, smart phone is using camera "app" and running the app using its processor, so the processor has to run the app and save let say 8MP picture from your smart phone to your memory card and this take a lot of processing power
so when the smart phone can achieve zero shutter lag, it mean it has fast processor and good amount of ram, and good writing speed...another strategy to promote sales
but in the case of digital camera, it majorly depends on the memory card speed and the faster the card the lesser you fell the shutter lag, try a Class 4 card and a UHS Class 10 card, you know the kick, btw who want to use a camera with shutter lag?

Maybe it's not really zero shutter lag.

Or they are using some continuous picture picture taking and when you press the shutter, the image say 0.05s before you pressed the shutter will be saved. Some digital cameras have this feature.

Higher end DSLRs use mechanical shutters, Shutter lag is inevitable and will never math electronic cut off shutter.

i would say that zero shutter lag is just a term used for smart phone, as they only achieve the speed,
while for dslr/or any current (maybe just maybe not all) camera has it. means its not a "thing" to be proud of. its something thats already been there since..

2gb ram in a phone is something new, while 2gb ram in pc is soo yesterday - example