A
It really depends on your point of view.
From the outside, the "script kiddie" is, nominally, the wannabe attacker who uses tools written by other people (the "scripts"), without really understanding what is going on. Everybody uses tools written by other people (if only operating systems, C compilers, libraries...), but some people have a certain understanding of how things work internally, and could, at least potentially (if free time was free), rewrite these tools from scratch.
The script kiddie himself does not think of himself as a "script kiddie", of course. In his view, he is an "elite hacker", and the other people are script kiddies. The expression "script kiddie" is meant as a disparaging designation, to insist on the alleged youth of the individual and its associated inherent shame. To consider youth as shameful by nature, you have to be young. Old people don't think of youth as a disgusting fact to hide, but as a lost treasure. When somebody uses the expression "script kiddie" too often, you can often infer that this somebody is himself not very old, and a metaphorical scripty smell probably lingers around his person.
A more neutral, less emotionally charged classification would be about competence. Attackers are more or less competent at what they do. Just like anybody. The less competent attackers, which other script kiddies are prone to point out and mock as "script kiddies", will run their tools (collected on the Internet), and if the off-the-shelf tools don't succeed in the attack, they soon give up. More competent attackers will adapt their tools to the specific situation; they see the tools more as a generic framework for attacks than the actual instruments.
Given the above, to avoid being seen as a script kiddie, the trick is to distantiate yourself from the kiddie term, not from the script. Scripts, and, more generally, tools, are neutral. It is the maturity of your reactions, or lack thereof, which will mark you as a script kiddie or not. Despite what is usually believed on the subject, it has very little to do with technical skill; it is a matter of communication, of public relations. Be cool, don't whine, and you will never be a script kiddie.