저(는) means making youself lower than the addressee in order to show your respect toward the addresse. it's kind of humble version of 'I'.
나(는) is just neutral (but using it when talking to much elder or much more respected person than yourself can be quite rude).
'요' means speaking politely in order to show your respect toward the addresse.
and you just dropp '요' if you really are on close terms with your addressee - this is how you get the 'intimacy' you wrote about in your question.
so, in the example Heesob Park provided, one'd rather not make yourself lower to show his(her) respect to an unfamiliar person which is younger than him(her), but one would add a polite ending in oder not to be rude toward his addressee.
hope my comment was of some help ^^