pen·ance (pĕn’əns)
n.
- An act of self-mortification or devotion performed voluntarily to show sorrow for a sin or other wrongdoing.
- A sacrament in some Christian churches that includes contrition, confession to a priest, acceptance of punishment, and absolution. Also called reconciliation.
tr.v., -anced, -anc·ing, -anc·es.
To impose penance upon.
[Middle English, from Old French, from Latin paenitentia, penitence, from paenitēns, paenitent-, penitent. See penitent.]
Indulgences firstly have nothing to do with specifically being sorry for sin. What they DO have specifically to do with is removing part or all of the TEMPORAL punishment due to your sin or the sins of others.
Rather like you don’t have to be sorry for having spilt a glass of milk, but if you’ve spilt it you DO need to clean it up, and you can clean up milk that someone else has spilled.
Secondly, apart from the Sacrament of confession you can set the conditions of your own penances - what you do as penance, for how long you do it, etc.
Indulgences are set only by the Popes, and the conditions for obtaining them are listed in such places as the Enchiridion of Indulgences. Only specific acts, performed under certain conditions, have indulgences attached to them.
Thirdly penance, on my understanding applies only to your own sins. You can’t really perform penance for the sins of another. You can perform SACRIFICES on their behalf, but this isn’t done directly to atone for their sins, they need to do that for themselves.
You can, however, obtain indulgences for the Souls in Purgatory (or indeed the soul of a specific deceased person) as well as yourself, though not for other living persons.
I’m sure I’ll be corrected if I’m wrong on some of this.