Stolons (in A and B) are long, slender horizontal stems running above-ground; they often bear adventitious roots. Stolons enable vegetative propagation of the plant: when the connections between nodes wither, this gives rise to several new plants (clones) at nodes/tips.
(A) represents stolons of strawberry (Fragaria )

Rhizomes (in B and C) are underground, horizontal stems; the leaves are often reduced to scales; rhizomes usually bear adventitious roots. They can serve as a storage organ and a mean of vegetative propagation; like stolons they can give rise to new plants (clones).
(C) represents a rhizome of spike-rush (Eleocharis )

(B) represents stolon and rhizome of Bermuda grass (Cynodon dactylon )