Roman Catholic Understanding
According to the Catechism of the Catholic Church:
Anyone who is aware of having committed a mortal sin must not receive
Holy Communion, even if he experiences deep contrition, without having
first received sacramental absolution (II.II.II.4.VII.1457)
I do not believe that the Roman Catholic understanding is that one's sins are not absolved if one fails to confess mortal sins in any case, but rather only in the case of mortal sins being knowingly concealed:
When Christ's faithful strive to confess all the sins that they can
remember, they undoubtedly place all of them before the divine mercy
for pardon. But those who fail to do so and knowingly withhold some,
place nothing before the divine goodness for remission through the
mediation of the priest, "for if the sick person is too ashamed to
show his wound to the doctor, the medicine cannot heal what it does
not know." (Ibid., II.II.II.4.VII.1456)
The Sacrament of Penance and Reconciliation, as it is called, also requires of the penitent "satisfaction":
Raised up from sin, the sinner must still recover his full spiritual
health by doing something more to make amends for the sin: he must
"make satisfaction for" or "expiate" his sins. This satisfaction is
also called "penance." (Ibid., II.II.II.4.VII.1459)
Eastern Orthodox Understanding
Within the eastern Church there is no such enumeration of "venial" and "mortal" sins. In general the Orthodox Church is less legalistic. All that is required of the penitent is:
Contrition for his sins, with a full purpose of amendment of life, faith in Jesus Christ, and hope in His mercy.1
The sacrament, which is referred to as the "Mystery of Penitence", is described as:
A sacrament in which he who confesses his sins is, on the outward
declaration of pardon by the priest, inwardly loosed from his sins by
Jesus Christ Himself.2
There is also a component of penitence in the Orthodox sacrament, but it is seen as less of a "satisfaction" and more of spiritual curative - this despite begin called sometimes by its Greek name, epithemia ("punishment", cf. 2 Corinthians 2:6):
Under this name are prescribed to the penitent, according as may be
requisite, divers particular exercises of piety, and divers
abstinences or privations, serving to efface the unrighteousness of
sin, and to subdue sinful habit; as, for instance, fasting beyond what
is prescribed for all, or for grievous sins suspension from the holy
communion for a given time.3
Although there are a large number of Church canons prescribing recommended epithemia for various offenses, priests have enormous discretion in deciding what sort of epithemia may be required, if any.
Anglican Understanding
My knowledge of Anglican ecclesiology is limited, but I understood that only Baptism and the Eucharist are recognized as Sacraments, as held by the Thirty-Nine Articles of Religion that are found in the Book of Common Prayer:
There are two Sacraments ordained of Christ our Lord in the Gospel,
that is to say, Baptism, and the Supper of the Lord.
Those five commonly called Sacraments, that is to say, Confirmation,
Penance, Orders, Matrimony, and extreme Unction, are not to be counted
for Sacraments of the Gospel, being such as have grown partly of the
corrupt following of the Apostles.4
1 The Longer Catechism of the Orthodox, Catholic, Eastern Church, Metropolitan Philaret of Moscow, Question 353
2 Ibid., Question 351
3 Ibid., Question 356
4 Article XXV, "Of the Sacraments"