The homonym for tail is tale. Tail refers to the rear part of an animal's body, while tale refers to a story or narrative.
TAIL = TALE ( as in a 'tall tale' or story )
tall story
a made up story
no Its a tall tale
A lie or a untrue story
"The story of Paul Bunyan is a tall tale."
You are probably intending on asking about a 'tall tale.' If it is about a tall tail, it might be about meerkats, they have very tall tails when they stick them up in the air. But a tall tale is a story that is so big in its descriptions of events and circumstances that is is hard to believe, sort of like bragging. A tall tale could be something like the story of Paul Bunion and his Ox.
A yarn is a story or tall tale. If you embroider a tale, you embellish or add onto it.
A tall tale. (or, a lie)
tall tale
tall tale