Sin and mistake could be differentiated by considering sin as something done deliberately and mistake as otherwise.
SIN
Sins can be differentiated into two: minor and major. But minor or major, a Muslim should avoid all sins and repent for the sins he had committed.
For a detailed view:
https://www.google.com/amp/s/www.isl.../fatwa/305404/
MISTAKE
Mistakes are pardoned and the person bears no sin for this.
For example, if you hurt someone unintentionally.
For more defined answer:
https://www.google.com/amp/s/www.isl.../fatwa/358213/
As to the question whether Allah will forgive a person who does a mistake or sin, Allah is the Most Merciful and the Most Forgiving.
Upon sincere repentance and seeking forgiveness, no matter how grave the sin was, Allah will forgive you.
جزاك الله خيرًا