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I believe the difference is that de Broglie's equation includes matter. Matter according to the de Broglie has wave-like behavior and this equation, therefore, is meant to include how to calculate the wavelength of an object of mass. The wave equation we worked with initally (c=wavelength*v) did not include mass or momentum.
The De Broglie equations includes the mass and velocity of a given particle while the normal wavelength equation can also be associated with light. You can tell which equation to use in a given situation based upon the parameters listed in the question.
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