* 姜 (jiāng) is the most common and general term for ginger. It's used for the root itself and in most situations.
* 生姜 (shēng jiāng) means "fresh ginger" and emphasizes that it's not dried.
* 干姜 (gān jiāng) means "dried ginger".
So, if you're talking about ginger in general, use "姜". If you want to specify fresh or dried, use "生姜" or "干姜" respectively.