first about the 1's aand 0's. HC is a relatively new way to format SD cards. there are SD, and SD(HC) cards. the card is physically identical, but many computers only 1 or 2 years old cannot read the new format. in order to read this new format, one gets an adapter that usually plugs into the usb port, and allows reading of the new sd(HC) format.

there is way too much information here:
http://en.wikipedia.org/wiki/Secure_Digital_card

now, physical size. the SD comes in three(?) different sizes. regular, tiny, and itty bitty. since most computers and reader adapters will only mechanically accept regular sized sd card, there are mechanical adapters to connect the smaller cards into the full sized(original) sd slot.

for a bit more confusion, there is an MMC card, which i think is the same size as the sd. read the wiki if you want to know about it.