The correct difference between $1^{st}$-order and $2^{nd}$-order reaction is that:

• A
  the rate of a $1^{st}$-order reaction does not depend on reactant concentration; the rate of a $2^{nd}$-order reaction does depend on reactant concentrations
• B
  the half-life of a $1^{st}$-order reaction does not depend on $[A]_0$; the half-life of a $2^{nd}$-order reaction does depend on $[A]_0$
• C
  $1^{st}$-order reaction can be catalyzed; a $2^{nd}$-order reaction cannot be catalyzed.
• D
  the rate of a $1^{st}$-order reaction does depend on reactant concentrations; the rate of a $2^{nd}$-order reaction does not depend on reactant concentrations