Excuse, condone, pardon, forgive, remit are comparable when meaning not to exact punishment or redress for (an offense) or from (an offender).
In polite use excuse, pardon, and forgive usually suggest a hope that one is not annoyed.
Both excuse and condone imply an overlooking or passing over either without censure or without adequate punishment; distinctively, one may excuse specific acts (as faults, omissions, or neglects) especially in social or conventional obligations or the person committing them, but one more often condones either a kind of behavior (as dishonesty, folly, or violence) or a course of conduct or an institution especially when constituting a grave breach of the moral code or a violation of law.
Pardon (opposed to punish ) and forgive (opposed to condemn ) are often employed interchangeably, but their implications may be distinct. One pardons when one frees from the penalty due for an offense or refrains from exacting punishment for it and one forgives when one gives up not only all claim to requital or retribution but also all resentment or desire for revenge.
Remit is a synonym only in the idiomatic phrase to remit sins, in which it means to free from the punishment due for one’s sins.