There are three main classification of clouds;
Cumuliform- from 'cotton-wool' fair weather cloud to the towering cumulonimbus of the thunderstorm; generally indicative of vertcal ascent due to an unstable atmosphere
Bases generally 2-6,000 feet, with cumulonimbus tops up to 30+,000 feet.

Stratiform clouds- flattened clouds either in a continuous sheet of separate elements; generally in a stable atmosphere from forced ascent either at a frontal slope or from orographic ascent