I rather don't like the word "repentance."
Repentance seems to have a restrictive, puritan meaning, while teshuvah has so many more connotations.
At any rate, the basic idea of teshuvah, which is not exactly repentance, is a return, a going back to the basic form.
That is teshuvah.
Now, the need to come back, to revert to the real basic form, means that one has left many things behind, good and bad things.
Tikkun is another step.
There is a saying that a person who never sins can do teshuvah; even a complete person can return to his basic form, which is on a higher level.
But tikkun means changing things and making them complete.
It is always connected with the world, with deeds, with life.
If I am doing any kind of tikkun, correction, then I have to be connected with myself, with my past, with the world.
It is not a process done in isolation.
Teshuvah is a much more solitary activity, in which a person turns in a certain way.
He may repent or not—in some cases there is no need for repentance.
There is a very profound saying that a person has to make teshuvah—and this is, by the way, one of the hardest cases—to make teshuvah not only on his sins, but on his virtues.
And it seems to be much harder to re-understand the good things that he did, to make them more complete.
In teshuvah, I am not so much involved with the world, but in tikkun there is always involvement.
–Rabbi Adin Steinsaltz
From "The Private Gate," an interview with Rabbi Adin Steinsaltz in Parabola magazine