Most nautical sails are not pushed by the wind; they’re pulled by the low pressure area created in front of the sail by the wind flowing over it, similar to an airplane wing. Solar sails do NOT work this way.
Sort of correct. Quibbles about what is a "push" and what is a "pull" in aeronautics.
Solar sails are not just pushed in the direction away from the Sun. By angling the sail to be off-perpendicular to the direction of the incoming light, the reflection effect of the photons to one side can provide a sideways push in any direction required.
Too bad it can't tack up-(solar)-wind though, like a sailboat can go as little as 45 degrees off the direction that the wind is coming from. That is because the photons do not interact to change direction as they pass by close to the sail, unlike the way air molecules flow around a boat's sail. The photons do not act like a cohesive fluid, but more like individual projectiles.
And, of course, solar sails don't have any sort of keel sticking into a different fluid with a different motion on the other side of some interface between the fluids, like a sailboat does. So, there are fewer vectors to work with to get a net "upwind" force on a solar sail spacecraft, compared to a sailboat moving through water with air blowing across the water's surface.
So, in sailing terms, a solar sail can't quite get to a "beam reach" and is basically a "broad reach" and "downwind" sail.
But, a solar sail still does have some maneuvering capabilities.