Can one use kindness as a synonym for politeness? What's the difference? Where do you draw the line between them?
I think this is a situation in which etymology is revealing.
The background of polite, according to the Online Etymology Dictionary, is:
mid-13c., from L. politus "refined, elegant," lit. "polished," pp. of polire "to polish, to make smooth." Used literally at first in English; sense of "elegant, cultured" is first recorded c.1500, that of "behaving courteously" is 1762.
Polite, both in its original literal usage and in its current usage, is more about superficial appearance. To be polite, one need only use polite words and manners. Nothing internal is necessary.
The history of kind, on the other hand, is related to internal goodness:
"friendly," from O.E. gecynde "natural, native, innate," originally "with the feeling of relatives for each other," from P.Gmc. gakundiz, from kunjan (see kin), with collective prefix ga- and abstract suffix -iz. Sense development from "with natural feelings," to "well-disposed" (c.1300), "benign, compassionate" (c.1300).
Ultimately, politeness tells you little about a person's character; it may be sincere, or it may be highly calculated. Kindness, though, is directly related to a person's character, and is quite difficult to fake.
The two concepts are orthogonal: politeness is about etiquette and manners, whilst kindness is about generosity and selflessness.
You can be polite whilst being unkind.
I'm terribly sorry, dear neighbour, but I am otherwise occupied at the moment. I will be unable to supply you with a cup of sugar at this time.
You can be impolite whilst being kind.
Here's your free cup of sugar, now bugger off and leave me alone.
I think "politeness" itself is divisible into two separate strains: one (that I would call "etiquette") is about following the norms of behaviour, however arbitrary or awkward they may be. The other (which you might call "consideration") is behaving in ways which tend to put other people at ease and make them comfortable.
There is an overlap, but they are different in intent and sometimes in result. The latter has a connection with kindness, the former does not.
Politeness is following the social conventions the person concerned would prefer (in some cases it would be addressing a female as Madam and in others as Ms). Kindness is making somebody feel better, whether it's a compliment or making somebody a cup of tea. I would say rudeness is never kind, but it is perfectly possible to be polite and unkind ('icily polite' is a common phrase for this.)
And you can be kind to animals (in England it's practically compulsory) but you can't be polite to them.
I agree with Philoto. Politeness has to do with a set of manners and practices belonging to a certain culture. However, many of the sources of the code of politeness or of good manners are either outdated or arbitrary. Therefore being polite may in no way involve being kind. For example, if I ask you for help, you can politely decline. You're being polite but not kind. Kindness has to do with doing good things or showing benevolence.
"Polite" has to do with presentation, "Kindness" has to do with act or action. My grandmother always thanked me politely as she took the winning card in a game, thus being both polite and doing it kindly at the same time even with a negative (for me) result presented. Sort of the opposite of taunting me for poor play which would have been both unpolite and unkind.