If someone is pubescent, they are going through puberty right now: the body is in the middle of changing from a child’s body to an adult’s. You will hear a pubescent boy, a pubescent girl. It is a describing word, and it belongs to doctors, writers, and careful talk, not to the playground. Friends are more likely to say “he’s going through puberty” or just name the age. You can also use it as a noun for that young person, though that sounds even more bookish. Though actually, biologists also call a plant pubescent when a leaf or stem is covered with very fine, soft hair, like down. That is the old Latin picture coming through — becoming hairy, becoming grown. Same word, two rooms: young people, and plants. It is not public, and it is not a fancy twin of teenager.