Within a context, the two may be different, yet the general descriptions are the same.
A level surface is measurably level; a horizontal surface simply implies the relative situation for a surface.
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Gravity pulls towards the center of the earth. Perpendicular to gravity is called "horizontal". Parallel to gravity is called "vertical".
A level is a tool that is placed on a solid surface. There is a string hanging on the level, and if it tilts, the surface isn't an even horizontal surface. If the string doesn't tilt, the surface is even.
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The straight level line is said to be horizontal.
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