That word is "faults" as correctly shown in the KJV. Not "sins" (ἁμαρτίας)
as shown in the modern versions, based upon the corrupted Critical Text. Only Young's Literal Translation has "trespasses".
KING JAMES BIBLE
Confess your faults* one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much.
RECEIVED TEXT
ἐξομολογεῖσθε ἀλλήλοις τὰ παραπτώματα*, καὶ εὔχεσθε ὑπὲρ ἀλλήλων, ὅπως ἰαθῆτε. πολὺ ἰσχύει δέησις δικαίου ἐνεργουμένη.
CRITICAL TEXT
ἐξομολογεῖσθε οὖν ἀλλήλοις τὰς ἁμαρτίας καὶ προσεύχεσθε / εὔχεσθε ὑπὲρ ἀλλήλων, ὅπως ἰαθῆτε. πολὺ ἰσχύει δέησις δικαίου ἐνεργουμένη.
*STRONGS NT 3900: παράπτωμα (paraptoma)
παράπτωμα, παραπτώματος, τό (παραπίπτω, which see);
1. properly, a fall beside or near something; but nowhere found in this sense.
2. tropically, a lapse or deviation from truth and uprightness; a sin, misdeed (R. V.trespass, 'differing from ἁμάρτημα