Stolon, offset and rhizome are different forms of stem modifications.

Stolon is underground stems which spread to new niches and when old plants die, new are formed. It is a creeper.

Offset is a lateral branch with short internodes and each node bearing a rosette of leaves and tuft of roots is found in aquatic plants.

The rhizome is an underground stem growing parallel to soil surface which is differentiated from roots in having scale leaves and auxiliary buds and helps in vegetative propagation.