  In much of the literature on linearized gravitational waves two completely
different notions are called transverse traceless modes and labelled
$h_{ab}^{TT}$, often in different sections of the same reference, without
realizing the underlying inconsistency. We compare and contrast the two notions
and find that the difference persists even at leading asymptotic order near
future null infinity $\mathit{I}^+$. We discuss why the distinction has
nonetheless remained largely unnoticed, and also point out that there are some
important physical effects where only one of the notions gives the correct
answer.
