"Jot down" implies a short little note, whereas "write down" might be something longer or more carefully thought out. The word "jot" is a reference the the smallest letter in the Greek alphabet, the "iota." You just might want to jot down this information in the English notebook that you carry around in your pocket.

Phil's right. When I write some little thing down quickly, especially in note form, or abbreviated, I feel I'm jotting it down. If I have time I might write it down properly, in full. Actually, a lot of the things I jot down I can't read! Maybe I should write them down properly!