A lateral branch with short internodes and each node bearing a rosette of leaves and tuft of adventitious roots is called 

Offset is lateral branch with short internodes and has adventitious roots and rosette of leaves at every node. Stolon is sub-aerial branch which is initially aerial and eventually becomes sub-aerial. Sucker is sub-aerial branch which is initially underground and eventually becomes sub aerial. Runner is horizontally growing branch or stem with several internodes and each node having adventitious roots and leaves.