Non-SDHC 4-GB cards do not conform to either standard and if they work in your device it is only by accident. The fault is in the original SD specification which could have gone up to 32G but they arbitrarily decided that 2 gigs should be enough for anybody.
The whole thing is another example of idiots being left in charge of the store.
AFAIK there is no such thing as 4G non-SDHC Micro-SD card. Hardly anybody is making any sort of non-SDHC card anymore, they just really only sort of work. I found that the only way I could use it was to format the card and then copy everything I wanted on it all at once. Anything copied at a later time showed as being there but actually was not accessible.