For us, I wouldn't say it is a difference between self righteousness and true righteousness. I guess I would say it is more like the difference between doing what He said outwardly and doing what He said inwardly (in spirit and truth.)
Outwardly, I can do the command to love others as myself. For instance, I give food to a hungry man. But inwardly, I can be seething and angry at him, thinking, he wouldn't be in the hungry position he's in if he didn't sit on the bench near the liquor store drinking all day, too drunk for anyone to hire him. So according to Jesus, I haven't loved him but have instead murdered him.
So I can do the right thing and give him some food. But I can't change my heart. I truly think, he has done this to himself, and if I'm having a bad day, that anger at him will make me walk by him instead of giving him some food. I'll think, no, I fed you three days in a row, im not feeding you again today, if you have enough money to get drunk, then get yourself some food.
So, how do I change my heart toward him? I have no idea. I can't. I can pretend, because he can't see my thoughts, but what's the use of pretending? It just makes me a hypocrite, saying/doing one thing outwardly while saying/doing the opposite inwardly. So you see, my righteousness has not exceeded the righteousness of a Pharisee as He has said it must.