A confraternity is a specifically Catholic group of laypeople. You can have a rosary confraternity, a scapular confraternity, and so on. There’s the Confraternity of the Precious Blood, the Confraternity of Holy Guardian Angels, the Confraternity of the Miraculous Medal, and so on. Basically you have some sort of sacramental, or pious practice, or act of charity, or special devotion, or so on, and build an [approved] organization around promoting that specific sacramental/devotion, living that way of life, and so on.
Fraternal organizations tend to be more broad in scope, from what I’ve seen, with multiple focuses. The Knights of Columbus are dedicated to supporting the church and serving the community, but it often takes the form of pancake breakfasts, fish frys, bingo, blood drives, food drives. There are Catholic fraternities like the Catholic Holy Family Society that do eyeglass drives, recognize Catholic educators, give scholarships to Catholic students, give grants to church projects— but primarily are a vehicle for providing life insurance to Catholics and their families. The Ancient Order of Hibernians is an Irish-American Catholic fraternity that had its roots in secret societies that protected Irish Catholics from religious persecution, and was established to help Catholic immigrants. It still does that-- but also is involved in political, social, and economic issues.
So I’d say that a confraternity is extremely focused and limited in its nature, and a fraternity is more broad and general.
