Fonts and typefaces have a container/content relationship. It’s true, look it up. Consider that font refers to the box that holds the math, which in turn defines or describes the style of a set of characters. Font is the file, the typeface is the stuff in the file.
Meanwhile, serif fonts shouldn’t necessarily be considered to be more legible or readable. At least, there isn’t any credible scientific literature available (assuming that link is credible).