I would presume that someone's 'third language' is the third language that he learned. However, according to Wikipedia, you are right that someone's second language is any language they learned after their first, not just the second language they learned.

What I mean is I was born speaking Wolof. Then I was taught French at 3. Then sometime when I was 15 I started to learn English. That along with German, I believe. That is why I say third.

Edit: Reading my answer to the original comment, you could have figured what I meant. Like when I read your username, I know ur means your, but maybe I should make a huge deal about it :). Lighten up, it's Wednesday.