High clouds are given surname of "cirro" or "cirrus." These clouds are ground at levels from 20,000 feet to 45, 000 feet. So you have cirrus clouds, cirrostratus, and cirrocumulus.
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Mid-level clouds are from about 7,000 feet to 23, 000 feet. They are given the name "alto" if they are not producing rain, and "nimbo" if they are.
Altocumulus are patchy white or gray layers. Altostratus clouds are gray and usually cover the whole sky. Nimbostratus clouds are dark and produce rain or snow.
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Low level clouds are found less than 7,000 feet. Stratocumulus clouds have a honeycomb look to them and allow for some peaks of sun. Stratus clouds usually cover the whole sky. They are thin.
Cumulus clouds are the pretty clouds that look like white cotton balls floating in the sky. And then you have Cumulonimbus, which are thunderstorms. From a distance they look like huge mountains or towers.
Check out this link with a great look at different cloud types from NOAA.