Tail has many definitions, including (1) the elongated appendage on the posterior part of some animals, (2) the hindmost part of something, (3) to follow, and (4) to provide with a tail. Tale means (1) a recital of events, (2) a story, or (3) a lie. So tale usually has to do with telling stories of some kind, while tail involves one thing being behind another.
He offers the example of peacocks’ tails, which grow larger and more colorful on healthy, parasite-free males. [WSJ Real Time Economics]
The Wild Bride tells the tale of a child won by the devil in a drunken pact with her father. [Irish Times]
I couldn’t make heads or tails of it. [Montreal Gazette]
Sanders has been performing for children for years as the Sourdough Cowboy, singing songs and telling tales. [Houston Chronicle]
The secret agents sought the truth in tailing suspected communist insurgents. [The Age]