Native American flutes and Native American style flutes are the same instrument. The name difference is due only to the Indian Arts and Crafts Act of 1990, which prohibits non-Native Americans from marketing and selling arts and crafts products as Native American-made. Therefore, only Native Americans would be legally allowed to sell their flutes as "Native American flutes", while others generally sell them as "Native American style flute" to indicate that they're the same instrument, but not made by a Native.
Though the two names help indicate who made a flute, it should not be used to judge the quality and workmanship of the instrument. It is possible for a Native American to create a low quality flute, or a non-Native to create a quality one.