Hi Luiz, They don't mean the same thing. When a person "leans over", it usually means to bend at the waist or hips so that you can reach something, like in your two examples: "My paper just fell on the floor! I leaned over and picked it up!" and "The floor got so stained with grease that I had to lean over and scrub it off!" "Lean across" means you bend at the waist or hips AND cross something (or someone) and possibly touch it. So this example: "She leaned across me so she could reach the phone!" means that she leaned and crossed my body and, possibly, touched me while doing so. A few more examples: "Simon pushed the chair, which leaned over and then fell." ("Lean over" can also apply to objects) "John leaned across the table to reach the glass on the other side." --> John crossed the table by leaning.