To "slip" is to lose control on a surface. To "slide" is to move along a surface with very little friction.
Children slide down a snow-covered hill on their sleds. Elevator doors slide open.
When you step onto an icy sidewalk and fall down, you have slipped on the ice. A wet floor is slippery. If you are holding something heavy it may slip out of your hands. When the clutch in your car starts to fail it will slip when you try to engage it.
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