Aside from the stereotype of females being overly emotional and teenagers being moody, many people think they understand these concepts, yet they have a tendency to confuse them. These words, mood and emotion, are not exactly synonyms, though they do stem from similar psychological origins.
Emotion: a brief intense psychological state that includes a) physiological, b) cognitive, and c) behavioral components. The physiological component of any emotion comes from a reaction in the autonomic nervous system--change in heart rate, change in respiration, change in blood flow and/or body temperature. The physiological reactions are similar for most emotions. In fact, feelings of hate and intense love lead to almost identical responses in the body's autonomic nervous system. The reason we can tell them apart comes from the cognitive and behavioral components. The cognitive component of emotion is your individual interpretation of your responses. This comes from memories, past experiences, social and environmental contexts, and your own attitudes regarding the object (person, place, thing, news, etc.) to which you are reacting. Sometimes a person can confuse one emotion for another, which could lead to interesting social implications. The behavioral component is how you communicate to others (and yourself) what it is you are feeling. This portion of emotion includes facial expressions. We are capable of over 20,000 different facial expressions, which might explain why it is not always easy to "read" someone else's emotions just from their face. Body posture, tone of voice, and even proxemics (the physical distance between individuals) also play a part in the behavioral component of emotion. All three of these--physiological, cognitive, and behavioral--come together so that we can experience a brief (not usually lasting more than a few seconds, rarely longer than a few minutes) emotion. The main reason emotions are so short lived is that our sympathetic nervous system cannot maintain a state of excited activity for too long without tapping out our body's reserves. It is our emergency fight-or-flight system, not meant to stay "on" all the time.
Mood: an extended, mild psychological state that persists after the intensity of an initial emotion ebbs. A mood is much milder than an emotion. While "happy" as an emotion only lasts a few seconds, the "happy" mood (contentment) can last several hours or even a few days. You no longer have the hyper energy you had the instant you found out that you won the lottery, but you remain pleasantly content in the days following your good fortune (barring some other even to lead to another emotion and then mood). Physiologically, your body continues to produce the hormones and/or neurotransmitters that lead to the initial emotion, but in much smaller doses. This mechanism allows us to slowly and safely back away from the chemicals that flooded our bodies in order to return to a state closer to homeostasis (balance) without the shock of "a drought following a flood."
An "emotional" individual, from a technically psychological perspective, is someone who experiences varied extreme reactions to life events in rapid succession. This often leads to exhaustion, as the body cannot maintain such excitability for too long. Yes, some individuals are naturally more excitable than others. No, excitability is not tied into gender. It is a personality trait--neuroticism. This trait is the sensitivity a person has to changes, good or bad. High neuroticism tends to mean more extreme emotions experienced more easily. Low neuroticism tends to mean fewer extreme emotional responses to life events, and more moderate emotions; a go-with-the-flow kind of person.
A "moody" person tends to hold on to the lingering effects of an emotion longer than the standard few hours or couple of days. They often do this by dwelling on the event that led to the initial emotion. This is one of the reasons depression and mania are "mood" disorders and not emotion disorders. The sadness (depression) persists for an extended period of time, usually more than 6 months for a conservative diagnosis. The excitability and irritability (mania) continues longer than "normal," often leading to irrational behaviors.
So, females are not necessarily emotional, but individuals scoring high on neuroticism have a tendency to experience extreme emotions more readily. Teenagers are not really moody, however, anyone who has a hard time letting go of events runs the risk of getting stuck in a mood rut.
Oh, and when you are "in the mood" for something, like chocolate or an action movie, that's a craving. In that case, the idea seems appealing to you, but it's not necessarily due to an emotional state. It could just be from suggestions (advertising, conversation, etc.) or motivation (internal or external, but most likely internal), or curiosity.