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SD, SDHC, and SDXC are just evolving iterations (standards) of higher capacity SD cards - there are no external physical differences.
I think SDHC starts at 16 or 32 GB, and I think it's SDXC beyond 64GB. Older card readers may not have support for the SDHC or SDXC standards, so when you get a new reader for using a high capacity SD card, make sure you buy one that supports the cards you use.. or just buy the one that supports the latest standards for the highest capacity cards (so you won't be prone to have to buy another one soon).
I've used several manufacturers of SD cards, and mostly, how reliable they are correlate well with the same companies' CF cards... the ones that make good CF cards make good SD cards... the ones who make unreliable CF cards are also likely to make less than reliable SD cards. Just stick with what you know with brands, and you'll be just fine