A combination of 5 Latin words gives us all 10 major cloud classifications:
Cirrus → curl of hair, feathery
Cumulus → heap, rounded
Stratus → layered
Nimbus → raining
Alto → middle
Based on cloud bases in the mid-latitudes.
Cirrus, Cirrostratus, Cirrocumulus
Altostratus, Altocumulus
Stratus, Nimbostratus, Stratocumulus, Cumulus
Cumulus Congestus, Cumulonimbus
Thin, wispy, silky clouds
Made of ice crystals
Blown by the wind
Thin clouds that cover a large portion (if not all) of the sky
Sheet-like
Made of ice crystals
Sometimes create optics like halos and sun dogs
Little white puffs
Made of ice crystals or water droplets
Typically in long rows
Sun dimly visible
Deck of layered gray clouds
Gray puffs (rounded elements)
Less than 1 km thick
Puffs are a little larger than the puffs of cirrocumulus
Commonly referred to as "cotton candy clouds"
White or gray base, but white top
Summer day clouds
Low, grayish uniform cloud deck
Typically covers the whole sky
Typically no precipitation (if any would be drizzle)
Lumpy clouds
Always appear in large groups covering most of the sky
Can look like cumulus but are a little flatter
Darker gray cloud
Light to moderate continuous precipitation (rain or snow)
Towering cumulus
Most often a large single cloud, but can grow into each other
Cauliflower tops
Showery activity
Lightning is not yet present
Thunderstorm cloud
Low base, but cloud tops can be as high as the tropopause
May have features such as an anvil (spread out on top) or Mammatus clouds (seen hanging beneath the anvil)