Reason and motive are often used interchangeably, but they are two distinct things.
A murderer driven by jealousy and rage has a motive: To cause harm to what he conceives as the source of his pain: his cheating wife. He is driven by his emotions to take an irrational action which he does not validate with logic (though he could exercise self-control and do that). His motive is jealousy, his reason? none.
If I take an umbrella on a sunny day my reason may be that the weather forecast said it would rain later in the day. In this case my decision is conscious and based on facts I have considered. My motive? the automatic distant emotion arising from the thought of being wet and having to run around if I get stuck in the rain without an umbrella. Both the reason and the motive are: not to get wet, but the reason is the conscious thought and the motive is the accompanying emotion.
If I rob a bank and force everyone to stay on the floor my reason is that if they are not on the floor they would be in a better position to resists me or to activate the alarm. The action of robbing a bank may be irrational, but the immediate decision to force people to stay on the floor is grounded in a conscious decision guided by facts. The reason to force people to stay on the floor, therefore, is to prevent resistance.
If I heard a speech I like a lot and feel an urge to stand up and applaud - I have a motive: A desire to express appreciation of something and to repay the wonderful individual who gave the speech. I may not be aware of why I feel an urge to stand up and applaud - but doing so has a motive. If, additionally, I am aware of why I want to applaud and the benefit it may bring me - then I stand up and act on it - it also becomes my reason for the action.
In other words: motive is referring to the emotional propelling force for an action while reason is referring to the conscious thinking process and conscious goal behind an action.
Every action has a motive, even if one is not aware of that motive; we cannot act without an emotion motivating an action; but not all actions have a reason. When someone is taking an action based on conscious thinking, the reason and the motive for it become two sides of the same coin (which is incidentally why "reason" and "motive" are often used interchangeably).
The question: "why did you do it?" is one, but its answer can be one of three: A reason (with a motive), a motive without a reason, or something which is entirely beyond a man's control (like an act of sheer insanity, or involuntary physical movement; neither of which have a reason nor a motive).
Let me break it down a bit more to make it clear: A reason necessarily comes with a motive and they are two sides of the same coin. How so? a conscious value judgement (deciding something is good for me or bad for me) is always coupled with an emotion. The emotion then serves as a motivation. For example: Why do I pursue a productive activity such as writing? The reason is a conscious decision to make money while satisfying a psychological need of self-esteem. I know that doing a productive activity is good for my life and I consciously decide to do it for this reason. The motivation is the emotion resulting from the subconscious recognition that productive activity has a positive effect on my life.
If my subconscious judgment, however, is not in line with my conscious thoughts then I would not be motivated to take the action. It is only to the extent that the subconscious is "persuaded" of the validity of the conscious value judgement that one can be motivated to take the action, and then the reason and the motive become one (or rather, two sides of the same thing).
Some may rationalize an action to try to provide a false reason for an action which actually had a different motive, in which case, the reason is false and the motive is real. For example: Say a guy is too shy to make a pass at a girl he likes. One day he decides to go to her house to talk. He tells the girl, and tries to convince himself that he went there to tell her that some class has been canceled, to save her time, but in fact that was not the reason he went there at all: He goes there to try to establish a relationship. In this case the so called "reason" is a rationalization. The motive is the real one and the action, in fact, has no reason, since the guy never made a conscious decision to make a pass at the girl.
If he did, in fact, tell himself in the privacy of his own mind that he is going there to try to start a relationship then it becomes his reason for going there, even if he hides it from others.
The reason for an action is not something that is always kept conscious. As I am writing this post, for example, I do not consciously think, at every moment, of the goal of writing it. The recognition of the goal stays in the background, as a thought and emotion. This does not mean that the action only has a motive but not a reason, just as one can know that 2+2=4 ALL the time, even though one rarely thinks about it. Knowing something consciously does not mean one constantly has to think about it. But for an action to have a reason the goal must be identified prior to the action. In many cases the reason is so well automatized one rarely stops to think about it. Why do you take your wallet when you go out? The reason is clear: to be able to buy whatever is necessary to function and enjoy the day (like a bus ticket, food coffee etc'). The reason is so clear one rarely stops to think of this consciously. Instead one just makes sure to take one's wallet before going out. This action does have a reason (and not just a motive) even though one does not stop to conscious reconsider the goal every single time.
It is enough that one is aware of the goal (of the value judgement) to make it a reason.
A motive can be good or bad, based on right ideas or wrong ideas. One can be motivated by an unrecognized desire for justice or by a desire to destroy out of envy. In either case, it is always better for one to be aware of the motive for an action and make a conscious decision about it, to the best of one's ability.