I always know that 歩く is the verb to use when talking about walking. But I'm aware the kanji 歩 has another verb 歩む. In WWWJDIC, the example sentence given is:
Bill climbed the ladder of success until he became the president of the company.
There is also this one line from the lyrics of the song 「未来へ」 by KIRORO:
It seems to me from these usage examples that 歩む is better suited to refer to the abstract type of walking, like walking down the path of life, while 歩く is used when referring to the actual act of walking on foot. Is this always true?