What distinguishes an “act of contrition” from a perfect act of contrition is the motivation for the contrition, (Theologians technically call it attrition) the act of contrition one usually recites when one is in the confessional, or as part of ones daily prayers goes something like this, (there are a few different translations published, so it varies from place to place.)
“Oh my God, I am sorry for having offended Thee, I detest all my sins because I dread the loss of heaven and the pains of hell, but most of all because they offend Thee my God who art so good.”
A perfect act of contrition, is the sorrow for ones sins because they are offensive to God.
As our sorrow for our sins is usually motivated by fear of hell, rather than simply because they offend God, we as Catholics take comfort in Jesus giving the Church, in His priesthood the authority to forgive sins. Which brings up another point, which James has already touched on. The priest does not forgive sins by his own authority, but rather God forgives the sins based on the priesthood of Christ, which He shares with the successors of the Apostles, who Jesus Himself granted the authority, as described previously.