Haven't quite understood; Didn't quite succeed.

Hi there,

Would you please confirm if my understanding of the next two quotes is correct? I consider b) is suitable for 1st and a) for 2nd, or...? If not, why, please. I made my choice just instinctively, though. I therefore would be curious to know why my choice is right in terms of understanding of native speaker or rules.

1) I haven't quite understood you.

a) I have understood you, but not good enough or not to significant/certain extent.

b) I have understood you, but not completely or absolutely.

2) At school they taught me how to be
So pure in thought and word and deed
They didn't quite succeed

a) They have succeeded, but not good enough or not to significant/certain extent.

b) They have succeeded, but not completely or absolutely.