  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 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.
