I see three different words when I look up "walk". Can someone explain why there are two and why one would be used instead of the other?
Difference between ayumu, sanpo and aruku
aruku (歩｛ある｝く) is a general term for to walk.
ayumu (歩｛あゆ｝む) is a little old-fashioned expression for to walk, especially to walk step by step, and it has a unique and something moral meanings different from aruku such as to make progress to a certain destination.
As for sanpo (散歩｛さんぽ｝), it is a noun which means a constitutional walk or a walk for relaxation.
To make a sanpo (散歩｛さんぽ｝) a verb suru (する) is attached like sanpo-suru (散歩｛さんぽ｝する).