  Let $F$ be a non-archimedean local field, $A$ be a central simple
$F$-algebra, and $G$ be the multiplicative group of $A$. To construct types for
supercuspidal representations of $G$, simple types by S\'echerre--Stevens and
Yu's construction are already known. In this paper, we compare these
constructions. In particular, we show essentially tame supercuspidal
representations of $G$ defined by Bushnell--Henniart are nothing but tame
supercuspidal representations defined by Yu.
