What’s the difference between unsatisfied and dissatisfied?

UNSATISFIED

When you are unsatisfied, you are not yet satisfied or fulfilled. There is incompleteness, a lack of something. You are not getting everything that is needed. Unsatisfied can refer to both people and things and ideas.

Children often feel an unsatisfied hunger for love and acceptance.
The defendant argued that the obligations under the contract were unsatisfied.

DISSATISFIED

When you are dissatisfied, you feel unhappy, displeased, disappointed, frustrated. Dissatisfied refers to how people feel.

Fred was dissatisfied with the wallpaper in his living-room.

A msn is standing by a window, looking out. A TV set is mounted on a wall. The wallpaper has a pattern of large flowers in black and white. The image illustrates the concept of dissatisfied.
Fred was dissatisfied with the wallpaper in his living-room

To sum up,

Unsatisfied = unfulfilled
Dissatisfied = annoyed, not happy

Some related words:

Dissatisfaction – disappointment, discontent
Dissatisfactory – causes dissatisfaction 
Unsatisfactory – inadequate
Unsatisfying – failing to satisfy

Read about uninterested and disinterested here.