The poser of the question's understanding is that there are sacramental and non-sacramental confessions.
This post aims to answer by starting with the definition of the Sacrament of Reconciliation or Penance and proceeding with an explanation of the process of Going to Confession. I believe with that, a clear understanding will emerge.
Penny Catechism, 112 & Excerpts for the Penny Catechism, 281-300
Q 112. By what means are sins forgiven?
A. Sins are forgiven principally by the Sacraments of Baptism and Penance.
Q 281. What is the Sacrament of Reconciliation (or Penance)?
A. Reconciliation (Penance) is a Sacrament whereby the sins, whether mortal or venial, which we have committed after Baptism are forgiven.
Q 283.When did our Lord institute the Sacrament of Penance?
A. Our Lord instituted the Sacrament of Penance when he breathed on his Apostles and gave them power to forgive sins, saying: 'Whose sins you shall forgive, they are forgiven.' John 20:23
Q 284. How does the priest forgive sins?
A. The priest forgives sins by the power of God, when he pronounces the words of absolution.
Q 295. What is confession?
A. Confession is to accuse ourselves of our sins to a priest approved by the Bishop.
This is a good place to define what a Sacrament (there are seven) is:
Penny Catechism, 249. What is a Sacrament?
A. A Sacrament is an outward sign of inward grace, ordained by Jesus Christ, by which grace is given to our souls.
Wondering why a penitent would want to confess their sins to a priest outside the sacrament of Reconciliation [there is no such process in the Church], from above, Confession is a penitent accusing themselves of their sins to a priest approved by the Bishop in the
Sacrament of Reconciliation.
Going to Confession
Elements of a good confession
To make a good confession, one should:
1. Pray first, asking God to help us.
2. Make a sincere examination of conscience to see how we have sinned since our last confession.
3. Confess our sins simply, with humility and honesty.
4. Make our act of contrition with heartfelt sorrow and a "firm purpose of amendment", being determined that we will avoid the occasions of sin.
5. Devoutly carry out the penance prescribed and pray in thanksgiving for God's overflowing love and mercy. - Source: A Simple Prayer Book | Catholic Truth Society.
Please see Catechism of the catholic Church, Article 4, The Sacrament of Penance and Reconciliation.
On the "sacramental seal" please see CCC 1467
1467 Given the delicacy and greatness of this ministry and the respect
due to persons, the Church declares that every priest who hears
confessions is bound under very severe penalties to keep absolute
secrecy regarding the sins that his penitents have confessed to him.
He can make no use of knowledge that confession gives him about
penitents' lives.[cf. CIC, can. 1388 § 1; CCEO, can. 1456.]
This secret, which admits of no exceptions, is called the
"sacramental seal", because what the penitent has made known to the priest remains "sealed" by the sacrament.
On priests and surplices and stoles, those belong to another question and answer.