As I begin to learn sonkeigo and kenjougo, I have come across several websites stating that levels of politeness and levels of respect are independent and not to be confused. I understand the concept of politeness without respect, but it seems to me that respect naturally contains the concept of politeness. (One would not be sloppy casual toward a respected person.) Furthering my confusion, an apparently reliable website gives the following example: “私はただいま自宅におります。… Addressee honorific. Your being at home does not affect anyone. Using おります is just politeness to the addressee.” That example’s explanation uses both “honorific” and “politeness” with respect to the same one word. Similarly, I’ve seen teineigo described as both the second politeness level and the first respect level.
My question is: would it be more accurate to say that sometimes expressions of politeness are independent of respect, but at other times a word indicates both? (I understand that keigo allows for various degrees of expressing both politeness and respect.)