Ok so when a nun becomes a nun (or a monk a monk,) is that a Sacrament?

Nope. There are 7 Sacraments , and religious vows are not among them. The priesthood is, of course, a Sacrament.

But aren't nuns married to Jesus? Wouldn't it be marriage?

Yes, but so is every Christian a spouse of Christ. Nuns image this in a more explicit way. She is an image of how the church is the bride of Christ.

Profession is an intensification of one's baptismal promises.
I was told that Solemn Profession, while not a sacrament does have some sort of quasi-sacramental character...but I sure can't explain that!

Okay, I'm going to take a stab at it. The Seven Sacraments are Saraments because they make a irrevocable mark on the soul and were instituted by Christ Himself. Religious orders grew up after Christ, so their vows were not instituted by Christ.

Vows can and do make a mark on the soul. But they are not Sacraments strictly speaking.

Oh sure, I think it's for sure a sacrament (little "s"). But many things today can be called "sacramental." Our Christian faith is lived, explained, and passed on to others through symbols and actions. In my book, that makes it sacramental... thus the Solemn Profession (and really, all vow ceremonies) for monks and sisters and nuns would be sacramental for sure, as would a variety of other rites and ceremonies. Praise be to God for the graced life we all lead!

And it's not so much marriage in the way that earthly marriage is. With marriage, the couple is the minister, and in order for it to be valid, it has to be physically consummated. I'm pretty sure that neither of these is the case with religious life. It's on a more supernatural plane than it is on a natural one; however, it doesn't negate the importance of vows, and the same gift of self that occurs in marriage, is very present in the evangelical counsels. The Sister or Brother still fully gives herself or himself to Christ.

The 7 Sacraments are for this life (on earth). They are channels of grace to help us get to heaven.

The Consecrated Life (vowed Religious Life) is not a Sacrament (big S) because it is a sign of the Life to Come! Isn't that awesome?!?!?!?!?!?!?!

This is the easiest explanation that I have heard.

Just for clarification, the sacrament occurs at the exchange of vows. Consummation makes the marriage indissoluble.

That is like a cool way to put it. Yeah cool....totally

Sacraments were instituted by Christ to give grace. Each sacrament has a sign; Baptism-Water; Communion- Eucharist, Confirmation-Oil, and so forth. Holy Orders is the ordination of a man to the priesthood or a Priest to bishop. The sign of holy orders is the roman collar. Holy Orders is a sacrament, vow taking is not.