Are the rules for VA pension benefits the same as for Medicaid?

No, they are not.  These are separate programs that have different qualification criteria and different rules concerning asset levels and divestment.  In addition, VA benefits are limited to families of veterans who served during time of war.  The benefits are, in general, either compensation, which is payment for disability tied to military service, or pension payments which are available to veterans, and spouses of deceased veterans, who qualify based upon either low levels of income or high medical expenses.