When you carry something, you move it from one place to another without letting it touch the ground.
1. They carry the packing case up the stairs and into the bedroom. 2. The students carried banners.
When you lift something, you move it upwards with your hands. After you have lifted it, you may carry it to a different place.
3. He jumped out of the cab to lift the two heavy suitcases from the boot.
4. The colonel lifted his cup, glared at it, set it down again.