Some psychologists have suggested that emotions are intense experiences whereas moods are mild experiences of pleasure or displeasure. However, one can be a little bit proud, or a little bit disappointed, and somehow we would not characterize these experiences as moods. On the other hand, one can be severely depressed and this intense experience is called a mood disorder. A better distinction between emotions and moods seems to be that emotions are specific experiences about something whereas moods are less specific and not about something particular. In a typical photo there is usually a prominent figure in the foreground that catches the attention and some other things are in the background.
Emotions are more like the prominent figure, moods more like the background.
The distinction is sometimes not very clear. For example, I might actually think of the sunshine and what a wonderful day it is after so many cloudy days. In this situation, we might say that we feel happy about the sunny day. However, I might be thinking about my lecture. But on a sunny day, I'll be more optimistic about the success of the lecture.