SDHC are the newer high capacity SD cards, anything 4gb and up is SDHC, so if it can do 4gb I guess it is :)
SDHC means Secure Digital High Capacity - but they come in several different physical sizes e.g. SDHC; Mini SDHC and Micro SDHC. The Micro card measures only 15mm x 10mm but you can get adapters to allow its use in slots for the larger cards providing that the device is SDHC compatible. They also come with differing data transfer rates and I guess the higher speed ones will be more expensive.
I have an 8 Gb, Class 4, Micro SDHC card in my htc TyTN II. The main reason for going to such a large capacity card is that the 'phone has GPS and I use it for walking trips. The large scale mapping software that I use takes up quite a lot of memory. Class 4 is the medium speed card and it works very well for me.