Stem Runners in vegetative propagation
Some plants, such as strawberries, have long stems that grow along the soil’s surface. They have buds on them. Adventitious (roots that appear on stems and leaves on plants) roots appear at the nodes where the buds are. When the nodes touch the soil, new shoots begin that grow into new plants. The runner continues to grow new stems and keeps running.
When you cut off and plant runner stems with buds on them, they will grow to become mature plants.
Great examples of runners include strawberries, bermudagrass, peppermint, and spider grass.
A stolon is not a runner although they are often used to mean one thing. Unlike the runner in the diagram above, a stolon is a fleshy and leafy stem that drops vertically downwards and takes roots where it touches a growing medium.
Source: 1. Asa Gray, How Plants Grow, A Simple Introduction to Structural Botany (New York: American Book Company, 1858) 39
http://etc.usf.edu/clipart/4800/4824/runner_1.htm Accessed on 23 June 2017