Wages are determined by the productivity of labor. A worker is paid the Discounted Marginal Revenue Product of his labor, i.e., the present value of the extra revenue his labor adds to a production process. If wages are lower in Vietnam than America it’s because labor productivity is lower there than in America.
If America established free trade with Vietnam, then American capitalist-entrepreneurs would invest in Vietnam . By raising the productivity of Vietnamese labor, the capital investment would move Vietnam wages up while American wages would not change (assuming no disinvestment in America). The equalization of wages would take time, so in transition American wages would remain higher than Vietnamese wages. The greater production of goods made possible by the capital investment implies that standards of living rise all around.