My husband (and his sisters) went through something similar. When he was 18 and leaving for college, his father told him that he had a half-sister that lived in that college's same town, the child of a previous relationship. It was the first time hubs had ever heard about her. (If hubs hadn't already been moving there, who knows when/if his father would've ever told him, but I digress). Hubs and his sisters had to adjust to another sister.
Hubs met her -- C -- and they get along, although they are not particularly close. We know of the major milestones, like marriage, birth, or when they change addresses, but compared to the relationship he has with his full sisters, it's not even close. And I'm pretty sure it never will be.
The thing is, no one tries to force it. I regularly contact C on holidays and her kids' birthdays, but my husband probably wouldn't bother if I didn't. His younger sister talks to her more regularly, and feels responsibility to know and be responsive to her because she's family. His older sister is different. The older sister is not thrilled to be replaced in the birth order, and doesn't talk to her at all, and has been rude to her in person. I know that their father wishes it could be different, but he knows that he can't force it. This situation was created a long time ago, and you can't go back in time and create a relationship that never existed in the first place.
Anyways, I think AOTB's absolutely right. Just meet them, but there's no need to put a lot of expectations on it. He may be a brother, but he was not raised as "your brother" -- in truth, he is from an entirely different family. Find out who he is, cause you're curious, and you'd like to know.
And then just let it go from there, into whatever relationship (friend, family, acquaintance) naturally forms.
P.S. I know what you mean when you say you don't know exactly how to define your family -- do you have one brother or more? -- although for an entirely different reason. I had a half-brother who was raised by his father, although we shared a mother. He was 10 years older than me, but we knew spent a lot of time together when I was very small, until he died unexpectedly when he was 18 and I was 8. Given that he died when I was so young, and that we didn't live in the same house when he was alive, I was esssentially raised as an only child. Yet, when people ask if I have any siblings, and I say "no" I always feel like I'm wrongly erasing his existence. But it's an honest answer.
My husband, by the way, always says he has two (rather than three sisters). Also, I think, an honest answer.