In Milnor's "Characteristics classes" there are two notation for the tangent bundle of a smooth manifold $M$. i.e. $\tau_M$ and $DM$. and $DM_x$ for tangent space. Why he uses of two different notation for one notion? I think both of them are $TM$ is new books notation.
Characteristics classes, page 14, Example 2. The tangent bundle $\tau_M$ of a smooth manifold $M$. The total space of $\tau_M$ is the manifold $DM$ consisting of all pairs $(x,v)$ with $x\in M$ and $v$ tangent to $M$ at $x$.