First of all, it might be helpful to get a firm grip on what actually goes on with conditionals. Basically, there are two tense systems that we use. The first is the tense system we generally use when using sentences with subordinate clauses that tell us about when something is going to happen. This is to say we use past verb forms to talk about past time, and we use present tenses to talk about present and future time. Within this type of conditional we can see all sorts of verb forms and modals in both clauses.
In the second system we can observe what is sometimes called backshifting of tense. What this means is that in these conditionals we use past tenses to talk about present and future time, and we use past perfect verb forms to talk about past time - even when we would normally expect to just see a past simple or continuous verb form. These backshifted conditionals have a different type of logic that is very difficult to accurately describe. This doesn't matter too much, because most languages have types of conditional which match these meanings very closely. So what you really need to do is enable learners to identify which ones they need. Effectively, backshifted conditionals are hypothetical, in the sense that when we use them we are more interested in discussing the idea at hand than we are directly in the immediate physical world.
When we use normal conditionals, what we are saying is that the situation described in the result clause WILL HAPPEN (or did happen etc), if the situation in the if-clause happens or did happen. When we use backshifted conditionals, we are saying that the situation in the result clause is a LOGICAL RESULT of the situation in the if-clause. However in this instance, it does not matter whether the situation in the if-clause ever happens or not. What we are emphasising is that the result clause is logically connected to the if-clause.
Students understand very quickly whether a given situation is hypothetical or not for them. All you need is a few examples.
However, here is the nasty truth of things. EFL books, and linguists in general know pretty much nothing about conditionals at all. However, we don't really like to say that we know nothing about something, especially if we have to write a reference grammar on it or teach it to students. For this reason, we like to make things up that are flagrantly not true or are only half true. It generally beats having nothing to say. This means that you need to learn what rubbish it is that you are expected to know. After that you need to know how to avoid teaching this at all costs.
The ugly untruth
This is the lie that you need to learn. Firstly, backshifted conditionals are sorted into two types. The second conditional uses the past simple to talk about the present of future. The third conditional is used to talk about past time.
The second conditional indicates that a given situation is UNLIKELY. The third conditional indicates that a given situation is IMPOSSIBLE. [Remember - none of this is true!!!!!]
Different writers use different words to describe this improbability. They use terms like modal remoteness and negative epistemic stance, or they just talk generally about improbability.
So, if you go for an interview to get onto a teacher-training course, what they want you to say is something like:
For the second conditional, I would give my students unlikely situations such as winning the lottery, and get them to make sentences about what they would do if they won.
For the third conditional, I would ask them about regrets they have in their life and how their lives would be different if they hadn't done those things.
In terms of explaining the difference, second conditionals indicate unlikely situations in the present or future and third conditionals indicate impossible situations in the past.
If you can remember that story, you will be able to pass the interview with flying colours.
Why you should never teach anyone this baloney
You may have noticed that you breathe when you sleep. However much you agree with this statement, you are unlikely to agree that you sleep when you breathe. Now we may use second and third conditionals when we think that a situation we're talking about is unlikely or impossible. But this is only because we cannot talk about these situations by describing the world directly. These situations are necessarily hypothetical. However, just because we wish to discuss things in a hypothetical manner does not mean that we think they are unlikely to happen. We often talk hypothetically for other reasons:
It is less direct and intrusive than talking directly about the world - especially if we are making suggestions to someone else or discussing a situation that doesn't directly affect us personally: Well, if you took the position at Kings college you'd be near your friends, and if you took ...
We may not want to bring the discussion round to whether the situation in the if-clause is actually going to happen or not. We may want to keep it hypothetical: So, if we offered you this position, what kind of salary would you be expecting?
- We may want to emphasise the logical connection between the if-clause and the result clause: If he had the measles he would be displaying exactly the symptoms that he is in fact displaying.
Notice that we cannot use a non-backshifted conditional for that last example. If you teach your students that we use backshifted conditionals because they indicate that the event described in the if-clause is unlikely, they will understand that last conditional to be saying exactly the reverse of what it's intending to say. Furthermore, it also means that your students may misunderstand people in interviews for example. Your students may think that the interviewer is not going to offer them the job when they ask about a hypothetical situation in which your student is given the job. Lastly, if your students ever become EFL teachers or write on sites like this one, they will unwittingly lie to all and sundry about the real meaning of backshifted conditionals.
So, in short, you need to learn this so you can parrot it at interviews. You then need to remember never to teach this deleterious piffle to your students.