It appears that this question has already been answered on Quora, so - as per this meta question - I'll provide an overview of what I've learned here:
- 字 and 文字 are, on their own, generally interchangeable.
- Compare "phone" and "telephone" in English.
- However, this may not be the case with compounds.
- For example, 漢字 is fine, but 漢文字 sounds strange.
Trivia: According to Wikipedia, these kanji were (and maybe still are?) used to make a distinction between characters with a single radical and those with multiple radicals in Chinese:
The title of the work draws a basic distinction between two types of characters, wén 文 and zì 字, the former being those composed of a single graphic element (such as shān 山 "mountain"), and the latter being those containing more than one such element (such as hǎo 好 "good" with 女 "woman" and 子 "child") which can be deconstructed into and analyzed in terms of their component elements.
However, I do not believe that this applies to modern Japanese (if it ever applied to Japanese at all).