The SDHC cards don't work in computers (but why???)
They work fine in my computer. That's because my Akasa 3.5" AK-ICR-01EB internal card reader is compatible. It cost me 9 UK pounds.
SDHC is a newer format, faster than plain SD and offering bigger memory sizes.
An SDHC card won't work in an older SD only slot, although it will physically fit, whether that slot happens to be in an internal card reader (fitted in a 3.5" computer drive bay), or a card slot on a laptop, or an external card reader, a camera, camcorder, phone, or other external device.
Cards 4 GB and larger are only available in the newer SDHC format. People buying SD cards should first check if all the slots they wish to use them in are compatible.
An SDHC compatible device will read from and write to both SD and SDHC cards, with lower performance using SD cards, but an older SD only device will only work with the older type.