Monte Carlo is basically taking repeated random samples until you get a good approximation of the value you're interested in. Gradient descent is more like what you describe, except you don't try "a bunch of different things" but keep trying the same thing until you have a result you think is good.

To give a silly example, Monte Carlo is like trying to guess the surface area of a dartboard by throwing darts at it and counting how many hit it, while gradient descent is like throwing darts at the board until you hit the center (or something you think is the center).