Clumping bamboo grows up in a single bunch of stalks with a large root ball that grows several feet underground. It does not tend to spread out much from its point of origin, and the clump of culms or stalks may only be a few feet across at its largest. This type of bamboo is more associated with mountain varieties, which need to concentrate their nutrients and resources.
Running or runner bamboo varieties do not stay in a single clump, but instead aggressively spread out to invade new territory. They send out runner roots that grow up into additional plants away from the parent growth. This type of bamboo can be difficult to control in gardens, and is more associated with the fast-growing river bamboo.
Timber bamboo is another general name for bamboo plants that grow large enough to be considered "trees," and are harvested for their fibers. This type of bamboo is made up of the varieties that grow up to around 20 feet or higher, such as the Phyllostachys variety. These bamboo plants grow in forests and are associated with runner bamboo.
Dwarf varieties are small types of bamboo plants that only grow several feet high or less. These can be used as ground cover and hedges. Dwarf bamboo shrubs are typically clumping, but dwarf varieties can also be runners. Dwarf varieties may be more suitable for colder climates.
Lucky bamboo should not be confused with true bamboo trees. Lucky bamboo is actually a type of water lily that resembles bamboo, but is a completely different species. This plant can grow in water and pebbles and makes a good indoor plant, but it is poisonous and cannot be harvested like bamboo.