The source of the previous confusion here is that in English the word "sandal" is in fact ambiguous. Vietnamese disambiguates footwear into "dép" (flip-flops affixed only to the front of the foot) and "giày" (shoes affixed to the whole foot). "Xăng đan" is from the french "sandale", and to native Vietnamese these whole-foot sandals are unequivocally "giày".
The second source of confusion is that young emigrants of Vietnam (like those of many other countries) often have experienced too limited a linguistic context to personally grasp onto these distinctions with certainty, yet just enough to have formed broad opinions on such questions.
No, "dép" only means slippers. Sandals are "giày". Basically any footwear without the back strap/wall are "dép", "guốc" if they're high heels (without the back strap). The rest are "giày" (sandals, shoes) or "giày cao gót" (high heels with back strap)
You can even say dép sandal, once again tangentmonkeys is only half right. :)