A regular space is a topological space in which points and closed sets can be separated by open sets; in other words, given a closed set $A$ and a point $x\notin A$ there are disjoint open sets $U$ and $V$ such that $x\in U$ and $A\subseteq V$

A $\T_3$ space is a regular $\T_0$ space. A $\T_3$ space is necessarily also $\T_2$ that is, Hausdorff.

Note that some authors make the opposite distinction between $\T_3$ spaces and regular spaces, that is, they define $\T_3$ spaces to be topological spaces in which points and closed sets can be separated by open sets, and then define regular spaces to be topological spaces that are both $\T_3$ and $\T_0$ (With these definitions, $\T_3$ does not imply $\T_2$ )