While the two terms are used interchangeably among people who have no need to distinguish between them, walking canes and walking sticks are two different things. The issue of walking canes vs. walking sticks is an issue mostly regarding their materials and use.
Walking canes are specifically meant to aid a person with an injured or weak leg. A support cane must bear weight, have a comfortable handle, and have a rubber tip on the bottom. These precautions ensure a useful mobility aid.
Canes can be crafted from wood, aluminum, bone, ebony and other sturdy materials. The word cane actually began to substitute the general term walking stick during the 1600s, when bamboo, Rattan and other dried reeds began to be used.
Walking sticks, in today's age, are more like hiking sticks. This is a broader category than support canes, because walking sticks can be almost any height, as they will be used from the side rather than from straight above. They don't necessarily need to have a comfortable hand and bear a great deal of weight.
Most companies that sell walking sticks market them for active purposes such as hiking and other outdoor adventures. Usually made out of wood, walking sticks reflect the natural, woodsy feel of a wilderness hike.