πίστιν – pistin (faith) This word can mean ‘confidence’, ‘assurance’, or a recognition of authority. Its use here seems to indicate that the four men who carried their companion to Jesus did so out of confidence that he would be able to make a difference. Jesus rewards those who recognize him.
The offer of forgiveness comes not from a recognition of the person on the pallet, but from a recognition of those who had brought him. Jesus sees the faith of the pallet carters
The word here translated as son is actually a gender neutral word for child: Τέκνον. A more literal translation is: “My child, your sins have left you.” The same word translated as “forgiveness” above also is used to indicate a change of legal status. A modern rendition could be: “Your criminal charges have been dismissed.”
ἁμαρτίαι – hamartai The word for sin is used twice in the first chapter and again here without any characterization about what the sin was or why it was important. The word implies an error, or a misdemeanor infraction of law, but also implies evil, poor faith, or bad intent. The first chapter speaks of the “remission” of sins, which would be like a civil process of clearing of the books of these infractions, and mentions later that the people of Judea were “confessing” their sins, which also sounds like a judicial or civil process.