Bright children will exhibit curiosity about almost any topic, asking questions, exploring, and wanting to know more; they will take it beyond just an immediate interest in a topic. Bright children want to know a lot more about a topic than may be initially and superficially presented, and they will display the initiative to learn more than other children. Gifted children take it several steps further, not only wanting to know about the topic, but to truly understand the topic from the inside out. Gifted children might often exhibit an infactuation or obsession with a topic that goes on for long periods of time, and often results in such an understanding of the topic that they can predict outcomes related to the topic or can extrapolate their knowledge of that topic to other topics. Their focus on learning the topic can be so intense that they have a hard time focusing on other topics until they've adequately satisfied their curiosity in the first topic (one of the reasons that gifted children don't automatically get good grades).
While bright children might research a topic to explore their curiosity, gifted children will initiate projects and experiments to test their preductions and assumptions about the topic. The topics of their interests don't have to be academic: our daughter often obsesses over issues with her friends, and took learning to drive extremely seriously (fortunately for us, way more seriously than most teens do). When gifted children come across a topic that interests them, they will latch on and it's often difficult (to say the least) to divert their attention. Our son is a part-time intern for a software company and we were recently told by his supervisor that he is incredibly detailed oriented. This attention to detail (when learning any topic) goes way back to his interest in topics from bats (the flying rodent kind) to reading (series of books) and more.
In summary, gifted children have a curiosity that goes way beyond that of other children, and (often) obsessively beyond that of bright children. If your child displays such an infatuation with a topic, and their outcome is an amazingly thorough understanding of the topic, it might be an indicator that they are gifted.