I'd say that "unfazed" and "unphased" have different meanings because they are negations of different verbs. Unfazed - not fazed, as in bibliolept's post and your example. Unphased - out of phase or no longer in phase, from the meaning of "phase" in particle physics: Wikipedia - Phase (Waves) Edit: sorry, the link did not work the first time. More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.