Studs are vertical boards, usually 2-by-4s, that make up the frame of the wall. Attaching curtain rod brackets to studs provides extra strength. When drilling a screw into a wall surface that's not backed by a stud, it has nothing to hold on to, and even a lightweight curtain will pull the screw out of the wall. With a stud, the screws "grab" the wood and are much harder to pull out. Drywall and wood walls are weaker than concrete, but even concrete walls can't hold up heavy curtains if the screws aren't secure. Locate studs no matter what the wall is made of when hanging heavy curtains, if possible.
When curtains place weight on a screw, the curtains pull on the screw in two ways. Tension is when the curtain pulls the screw straight out from the wall. Shear is when the curtain pulls down on the screw. Curtains create tension and shear when hanging. Each type of anchor has a limit to how much tension and shear it can handle when in the wall. Weigh the curtains and makes sure the screws are rated to handle the weight. For example, if the curtain weighs 20 lbs. and each anchor holds 5 lbs. of weight, the bracket will no fewer than four anchors. Purchase a bracket that has four holes for screws, and attach the bracket to studs for added support.
After placing expansion anchors into the wall, the screw goes inside the anchor. The screw spreads the anchor, placing extra pressure on the wall or stud. Threaded anchors are metal or plastic and have a point that spreads after installation. Both have a low-tension threshold of 10 to 20 lbs. and a shear threshold of 15 to 25 lbs. The difference depends on the thickness of the wall. Although stronger in concrete, expansion and threaded anchors do not hold up in drywall unless using a stud.
Molly bolts were designed for installation directly into walls without studs. Molly bolts have teeth that grab onto the inside of a wall. They have a tension threshold of 25 to 60 lbs. and a shear threshold of 25 to 65 lbs. Molly bolts come in different lengths. The smaller the bolt, the less it holds.
Plastic toggles look like anchors, and installation requires pushing the anchor into a hole and then pulling back so the "wings" open. Plastic toggles have a tension threshold between 20 and 25 lbs. and a shear threshold between 30 and 50 lbs. Metal toggles, also called toggle bolts, have metal wings that grip the back of a wall. Toggle bolts have a tension threshold between 35 and 135 lbs. and a shear threshold between 45 and 150 lbs. It all depends on the size of the bolt and the thickness of the wall.