No, they are different!  Red velvet is made with vinegar and buttermilk, which react with baking soda to make it rise.  The red color comes from the reaction between the cocoa powder and the acidic vinegar and buttermilk.  For a brighter shade of red in your red velvet, you can add red food coloring.  Unlike red velvet, most chocolate cakes are made with baking powder and don't contain food coloring.  Read more about the differences between chocolate and red velvet cakes here.