They're both points of equilibrium; Lagrange points are both stable (like a ball rolling in a half-pipe) and unstable (like a pencil standing on its tip) equilibriums. A stable equilibrium means that when an object in that point is displaced, it starts oscillating around that point, and unstable means that an object at that point, when displaced, will uncontrollably move away from it, unless you push it back onto that point.

Well, the Newtonian gravitational potential is far more simple to deal with than something like super hot plasma confined by a strong magnetic field. But yeah, you typically do not want that moving around the place, so I presume it's a stable equilibrium.

Does the reasoning behind it all seem to make sense, or does it seem like meaningless sci-fi word-salad? I don't understand enough to know.