Uhm, looking at pictures those beignets look "squishy", spongelike. It reminds me of spanish Buñuelos, which might be similar to Malassadas (haven't tried the last ones). Definitely not churros, which are a little crunchier.
They are all three fried dough, but churros are more stock like. We call them cinnamon sticks. Beignets are more melt in your mouth with deep hollow pockets. Kind of square shape and have confectioners sugar. Both can have fruit, chocolate, dips, and filling. While Portuguese doughnuts are dipped in granulated sugar and are more fried cake like. Kind of a cross of the other two.