Deontology is a morally absolute system and is identified with Immanuel Kant. Under his ethical system, people should follow universal moral laws without worrying about the consequences. Consequentialism, in contrast, is the kind of moral system proposed by utilitarian philosophers such as John Stuart Mill. As its name suggests, it allows individuals to take into account the context of a moral lapse and what the consequences of following a moral law might be in a particular situation. Consequentialists, for example, might say that while lying is breaking universal moral laws, there are instances when it is the better choice than truth-telling, such as when slaves catchers were looking for an escaped slave or Nazis were searching for Jews.
Y0u, of course, have to make your own decision about which way is better, but in the case of the single mother with two children, it seems best to act as a consequentialist and weigh the consequences of turning her in for embezzlement. This way, you have the opportunity to determine how much she is stealing against her needs as well as what the consequences might be to her children, innocent bystanders, were she to lose her job or be imprisoned. This is the harder of the two ethical systems, as it is far less black and white than deontology and involves making moral judgments. In fact, a deontological thinker would argue that is is not up to us or even possible for us to try to determine outcome: we merely need to do what is right and trust that it will work out. As Kant said in Groundwork of the Metaphysics of Morals,
I ought never to act except in such a way that I could also will that my maxim should become a universal law.
As the average person would never want embezzlement to become a universal law or, as we might say, an accepted ethical practice, there is no choice but to turn the mother in for her behavior. If we hate embezzlement, we must root the embezzlers in our midst.
Mill, however, refutes that notion in Utilitarianism's first chapter, arguing,
All action is for the sake of some end, and rules of action, it seems natural to suppose, must take their whole character and colour from the end to which they are subservient .... A test of right and wrong must be the means, one would think, of ascertaining what is right or wrong, and not a consequence of having already ascertained it.
It does seem to me important to understand the ends or goals of why a person is acting in way that may seem immoral before one passes judgment. If a person is embezzling funds to buy food for her children, that is a different goal and deserves a different set of reactions than embezzling funds to take expensive vacations, for example.