It may be more of how the word is currently used - in popular culture, respect is frequently used as a synonym for politeness.
I think it's more than just pop culture because I think the notion of politeness is rooted in basic respect. Why do we behave politely? Why behave politely to people you don't know, and you will never meet again? It's not for your own good - you get no 'recompense' for it. It's because politeness is a form of the golden rule, to behave towards other as you would have them behave to you. To get to that position, you must lend everyone - regardless of your acquaintance with them - a certain degree of inherent value
- a basic value equivalent of you. You aren't polite
to other animals, plants, inanimate objects because you do not imbue them with that unit of inherent value, that inherent value is what I am calling 'basic respect'.
Just to give you an example here. Imagine you were walking through a door and someone was coming up behind you, so you held the door open for them to pass through. Imagine that person walked through without so much as glancing at you - let alone smiling, nodding, saying thank you - just waltzed past as if you weren't even there. Was that 'rude' of them? Why? It's not really rude because they didn't ask you to open the door, you did it of your own volition. They can't be obliged to 'pay' you for something they never asked for. The reason why you feel unhappy that the person ignored you is because they're not paying you basic respect, acknowledging you as a human.
Deeper respect is through familiarity, through seeing a person being steadfast in a characteristic you place value in. Some might value a guy's willingness to laugh in the face of danger and to fight even when the odds are against. Some might value a constant regard for the other person, a willingness to humble themselves to bolster the other. This is a respect that's earned by steadfastness of character.
That's my take on it, anyway - I see politeness as coming after the basic level of respect you intrinsically lend to all other human actors.