“If I had studied, I would have a good grade.”

So, the question is: What is the difference between these two statements?

"If I had studied, I would have gotten a good grade."
and
“If I had studied, I would have a good grade.”

For instance, I would say that the former would be appropriate if receiving a bad grade happened in the past. The latter implies that having a grade is still a current state. For instance, I could imagine a conversation like this:

"So, are you an A-student or a B-student?"

"I'm actually a C-student now. If I had studied, I would have a good grade."

In other words, having a bad grade is his current state, so it would make sense to say "I would have a good grade now, but I don't."

This would make more sense for health inspection grades for restaurants or grading of hotels. Some restaurants are rated "B" by the health department, and that status would remain so until the next inspection. So, until then that restaurant is a "B" restaurant. The owner could say, "If we had cleaned our kitchen better, we would have a good grade now."

"If I had studied, I would have gotten a good grade." (but I didn't - it didn't happen)
“If I had studied, I would have a good grade.” (but I don't - ie present)

"Would" indicates a non-real idea (what looks like the past tense sometimes meaning it won't or didn't happen eg If I were rich..) ; "have gotten" indicates the past (a perfect infinitive if you will).

Just to add to what jayles and dyske have said, this is what in EFL and ESL we call a mixed conditional. The first part "If I had studied" is like a 3rd conditional (unreal event in the past), and the second part, "I would have a good grade", is like a 2nd conditional (unreal event in the present). So there's an unfulfilled condition in the past leading to an unfulfilled result in the present. It's what I call a 3:2 mixed conditional. (Some grammarians refer to unreal as counterfactual, but it's too much of a mouthful for me!)

A pure second conditional would have both an unreal present (or future) condition and result: "If I studied hard, I would get a good grade"

We can also have the opposite: a 2:3 mixed conditional, where a present (or more likely general) condition has a past result. - "If I wasn't (or weren't for the purists) so lazy, I would have studied harder. (But I am lazy (by nature), so I didn't study).

I've written quite a full explanation of 3rd and mixed conditionals, with exercises and a discussion of the "wasn't/weren't" issue (for foreign learners) here : http://random-idea-english.blogspot.com/2011/02/more-on-condtionals-third-and-mixed.html

One last point regarding the original question - in "I would have a good grade", "have" is certainly possessive, but it's not an auxiliary: it's the main (or lexical verb). The auxiliary here is "would". On the other hand "have" (or rather "had") is an auxiliary in the first part, "If I had studied" and (together with "would") in the 3rd conditional result clause "I would have gotten a good grade", where "study" and "get" are the main (lexical) verbs, respectively.

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