Teenage means belonging to the years between thirteen and nineteen. The numbers that end in teen.
That is the whole definition, which is why twelve and twenty are outside it however the person behaves. It goes before a noun, so a teenage daughter or teenage years. The noun is a teenager, a word invented in the 1940s along with the whole idea of teenagers as a separate market. Teens as a noun means the same period, so being in your teens covers all seven years.
1adjectiveteenageRelating to a person aged between thirteen and nineteen.
“They have two teenage sons.”
From -teen + age. First attested in 1921.
Etymology from Wiktionary, CC BY-SA