Tangent bundle at a set

Question

If we have a set $X=A\cup B$ and $Y= A\cap B$. What is the difference between $TY$ (the tangent bundle of $Y$) and $T_{Y}X$ (the tangent bundle of $X$ at $Y$)? That is, $Y$ is subset of $X$, so I can not understand what we mean by tangent bundle of $X$ at $Y$ and how it is different from tangent bundle of $Y$.