I’m definitely not the most qualified person to respond, but I’m discerning monastic life and have done a fair bit of research on a university level concerning monasticism.
The Cistercian Order was reformed in the 17th century. The reformed Cistercians are commonly known as Trappists or OSCO (Order of Cistercians of the Strict Observance). Apart from popular belief, St. Bernard of Clairvaux did not actually found the order, but he heavily influenced the reform. That’s correct! Cistercians are a reform themselves. They were Benedictines in the town of Cîteaux (Latin Name: Cistercium). To answer your question “what’s the difference?” Well, there isn’t a whole lot. Cistercians follow the Rule of Saint Benedict like most western monks except Carthusians. Benedictines became lax by the 10th century so the Cistercians became strict. The Cistercians became lax by the 17th century so the Trappists became strict. Nowadays there are monasteries and abbeys in most orders that are lax, strict, or somewhere in between.
I can’t speak a whole lot about the your situation or the Benedictines you know since I don’t have a ton of information about either. One thing to be careful of is that some religious (monks, friars, sisters, etc.) say, “You’d make a great XYZ!” because they see some kind of holiness in you. The thing is, every saint could potentially make a great XYZ because they were so holy. But the question is, what XYZ would you make the best of? (Rather, what would make you the best?) St. Thomas Aquinas could have been a holy Benedictine, but he was called to be holier as a Dominican. Also, as someone else mentioned, God uses our natural inclinations? If you don’t find monastic life attractive it might not be for you. (I realized you may actually find it attractive, but this is generalized for the sake of anyone reading.)
Salvation and Monasticism:
I would first warn you from saying, “I don’t want to be damned if I become a monk.” You can rest in assurance per the Magesterium that monastic life is a perfectly acceptable manner of achieving salvation. Otherwise, the church would condemn that life, not promote it. Instead, the church canonizes monks and nuns and shows their lives to be exemplary Christian lives. So the “become a monk” part is not the issue. The issue of damnation may arise only at the “if I” part of the statement. Monasticism may not be your vocation and if you choose monastic life knowing it is against God’s will, you have obviously committed a sin (likely a grave one too).
Purpose of Monks:
If the church is a body, contemplatives are the muscles to the heart which keep the pulse and graces flowing to the rest of the body. (Pius XI, St. John Paul II, and many popes hold this view.) They spend their live constantly praying and sacrificing for those who have no one to pray for them. While missionary orders administer to the Church Militant (living on Earth), monks are the missionaries to the Church Suffering (living in Purgatory). Many think all monks do is pray and, hopefully, they’re CORRECT! Every action of a Christians life should be a prayer in some regard. St. Benedict says, “Nothing should be preferred to the Work of God (Opus Dei).” He explicitly uses Opus Dei and the Divine Office synonymously. For monks, rising at 4 am every day and chanting the entire psalter is their labor of love (naturally they physically work as well). On a spiritual level, it is no less work than missionaries. This is why St. Therese of Liseaux (cloistered Discalced Carmelite Nun) is the patron saint of missionaries along side of St. Francis Xavier.
Monks can often practice the seven spiritual works of mercy on a much deeper level than active religious might be able to. They write letters/books, give retreats, pray with/for others, administer sacramentally and spiritually to visitors and brother monks in order to 1) instruct the ignorant, 2) counsel the doubtful, 3) comfort the afflicted, and 4) admonish the sinner. Living with the same men in the same place for your entire life, a monk learns to mercifully 5) bear wrongs patiently and 6) forgive offenses willingly. And arguably the greatest act of mercy that can be done amongst the physical and spiritual is 7) praying for the living and the dead.
I’m not going to go into great detail on how intercession and grace works now (that’s for another forum), but monasticism is not avoiding the world. Monasticism is the embrace of both physical and spiritual worlds from a great distance. Monks must be prepared to never know the good they did on Earth and to never have consolation in this life for the sake of the salvation of their souls and the souls of others. (For anyone wondering, acting for the sake of the salvation of your own souls is GOOD. It naturally comes about though when acting out of love for God and others.)
I sincerely hope this helped. You are surely in my prayers. Please keep me in yours.