Doesn the word rune refer to the symbols?
No, the word rune means “mysteries” and refers to the meaning behind the rune name and symbol. There were also runic symbols outside the futharks such as the sun wheel, and there are some hints that the healing powers of herbs were also thought runic in nature (see the Nine Worts Galdor). The word rune stave should be used to denote a symbol when not speaking of the myseteries the runic letter symbolizes.