Let $A$ and $B$ be two subgroups of the same group $G$. let

$$AB=\{ab\,|\, a\in A,\, b\in B \}$$
and 
$$\langle A,B\rangle$$ the subgroup generated by $A$ and $B$. 

Are $AB$ and $\langle A,B\rangle$ the same as sets? My guess is no since the element $aba\in \langle A,B\rangle$ but it is not in $AB$, but I guess when $A$ and $B$ commute: $AB=BA$ then this is true. is this correct?