Learn English – The second and the third conditional, what’s the difference

The Three Conditionals (or sometimes Four Conditionals) provide perfectly adequate explanations of the sentences you cite.

So did what was taught in US high schools in my youth under the rubric Sequence of Tenses. (At least I think it did; I wasn't paying that much attention at the time.)

What needs to be kept in mind is that these are what I have elsewhere called ‘baby rules’. Students must master crawling before they walk and walking before they run, and rules of this sort are directed to crawling and walking. Your ordinary English class or English grammar textbook is a linguistic hothouse, where students are carefully isolated from uses which lie outside, and appear to violate, the rules they are learning. This provides a foothold on the language which permits the student to grow in mastery and confidence (and of course ‘self-esteem’, which is of great concern to modern educators) before they are released into the wild and must confront the horrors of real life: colloquial, business and literary English.

What tchrist (indignantly) and Barrie England (charitably) are concerned to point out (on ELU, where the audience is presumed to be sophisticated users) is that these rules are inadequate maps to large tracts of that wilderness; such sentences, for instance, as these:

If you’ll pick up the beer I’ll get the brats.
If you’d ever actually read Lévi-Strauss you wouldn’t say stupid things like that.
If it was me I’d give him what for.
If you actually look it up what he said was completely different.

Rules are for learning with; but once you’ve learned enough to walk on your own you can discard these crutches.

Start by dismissing the ‘first / second / third conditional’ notion from consideration—that is a ‘baby rule’ for introducing beginners to conditional constructions.

The sentence given in your quote may mean two different things: it may be (1) a tentative (hypothetical) conditional in the present tense with future reference, or (2) an open (possible) conditional in the past tense with future-in-past reference. This ambiguity is resolved in the discourse context.

• (1) If you asked me nicely, I might get you a drink; but right now you are behaving very rudely and you can get your own. —Here the past-form asked and might do not imply past reference but ‘modal remoteness’—that is, you are doubtful that the condition and its consequence will be realized.

• (2) I told you then that if you asked me nicely, I might get you a drink. —Here the past-form verbs do imply past reference; the sentence represents backshifted If you ask me nicely I may get you a drink, which implies that at the time of utterance you regarded the condition and consequence as future possibilities.

• Note, by the way, that the pre-backshift present-tense version may equally well be expressed as If you ask me nicely I might get you a drink if the MAY in the consequence clause represents possibility rather than permission. In that case, it will retain the same form, might, when backshifted. The use of modals is very complicated: it has been constantly changing for hundreds of years, and we are in the middle of what appears to be an acceleration of the change.

Your rewrite, however, will bear only one interpretation, a past counterfactual:

• If you had asked me nicely, I would have got^† you a drink. —Here the ‘double past’ in both verb constructions (had asked, would have got) marks the sentence as both past-tense and modally remote. This is understood to mean a ‘condition contrary to fact’: on the past occasion of which you are speaking both the condition (your asking nicely) and its consequence (my getting you a drink) failed to occur.

^†As user3169 and Lucien Sava point out, this is the correct past participle of get in BrE but must be gotten in AmE.