There are a lot of cloud types. Let’s start with the high altitude clouds.
Cirrus clouds are thin, wispy and feathery, composed of ice crystals.
Cirrocumulus have a puffy, patchy appearance and small spaces between clouds. These often form wave-like patterns.
Cirrostratus are light gray or white. Often thin with the sun or moon visible through them. They cover most of the sky.
Middle level clouds include altocumulus. Puffy, patchy appearance, usually with spaces between clouds.
Altostratus are light and uniform in appearance, generally covering most of the sky.
Low clouds include stratocumulus. Irregular masses of clouds, rolling or puffy in appearance, sometime with spaces between clouds.
Stratus are light or dark gray, generally uniform in appearance and covering most of the sky. Fog is a stratus cloud.
Cumulus appear puffy and look like cotton balls, popcorn or cauliflower.
Both low and middle, Nimbostratus are dark gray with precipitation falling from them. Bases are diffuse and difficult to determine because of falling precipitation.
Cumulonimbus are clouds with dark bases and tall billowing towers. These can have sharp well defined edges or an anvil-shaped top. Precipitation can obscure the base. This cloud can be accompanied by thunder.

There are more clouds types, follow the link.