I never really understood the difference, so can someone explain?

I've never heard this referring to me, myself, but I've heard other people being yelled at, with the person who was yelling saying something along the lines of ''You're only sorry that you got caught.'', but what do they usually mean by that?

I see it as if one gets caught, one gets caught.

What does ''sorry'' have to do with that?
What's the difference between someone who's actually sorry for something they've done vs. someone who's ''sorry they got caught''?

I am rather upset that I got myself caught stealing money from my mothers purse, I knew it was wrong but at the time being wrong was not enough to prevent me from doing the act, I am only sorry that I din't cover my ass enough to have my sister get blamed for it instead.  As I've grown over the years, my moral standing has changed and alongside it my character, and I can see the reprocusions of stealing the money from my mother more clearly, I see now that the act of thievery caused me to travel down a dark path of self righteousness and pure abandonment of altruistic thought.  I am happy that I got caught because they consequences are no longer in the present, but rather a mark in my past that reminds me of my past character.  I am grateful that through my selfish act I managed to grow to a point where I am no longer sorry for myself for getting caught, now regretful that I caused pain to someone without ever thinking of their feelings.

I think Alinstrings gave a pretty good example. Especially for the context it sounds like you're inquiring, the difference really lies in whether or not the person would feel bad/guilty after accomplishing the task they set out to do. If you feel bad after stealing, etc, then you know you're at least a tiny bit sorry (not sorry enough to not do it to begin with, but that's another story). If you get caught in an act and you're only thought is how you could've gotten away with it, not how you were prevented from doing something tragic, then it's more likely you're only 'sorry' that you got caught. 

All in all, people don't want  to look 'bad' to other people. So an apology can sometimes come off to someone as not genuine if they feel that the person would've been all too happy to actually get away with their crime. 

Obviously they wouldn't apologize to whom they were offending before they offended them.

But, there is a faint chance that the apology from one who was caught is the truth.

When someone is sorry for doing something, they want to take it back and not do it because they hurt themselves or others.

When someone is sorry for being caught, they are glad or happy they did what they did, regardless of hurting others, but they feel bad another person knows what they did.  They're sorry the person found out because they would have otherwise gotten away with it.

It mostly refers to cheating.  If I am dating a girl and I kiss another girl, I might feel bad that I did it because I know my girlfriend would be upset, angry, and hurt.  I would wish I never did it because I feel bad for evoking those emotions in my girlfriend and our relationship.

If I felt bad for being caught, that means I liked kissing the other girl, I'm glad I did it, I don't care if my girlfriend would be hurt enough because I got away with it and it wasn't an issue.  Then I get caught or someone tells and I suddenly feel bad because I was busted.  I'm still glad I kissed the other girl, I'm just unhappy my girlfriend knows now because she's angry at me.

Does that make sense?

Put another way:

When you say "you're only sorry because you got caught", it means "you are not actually sorry, you are just SAYING sorry because you have to, now that you're caught".

Ok thanks guys!
Now its more clear to me!