If you want to read a word $w$ with a PDA, and know if $w\in L$ or not, then you could:
put the letters of $w$ in the stack of the PDA until you read a $c$;
read the $c$ without changing the stack. If there is no $c$, then $w\notin L$;
read the remaining of $w$:
if you read another $c$, then $w\notin L$;
if the stack is empty before the end of $w$, then $w\...
The set of languages of type $3$ is a proper subset of the of languages of type $2$. In other words, a language of type $3$ is also a language of type $2$.
If some automaton can recognize languages of type $2$, then it can also recognize languages of type $3$.