No they are not the same ginger but they are related. The blooming ones are often called Butterfly Gingers and the spice one is usually called Ginger Root or Edible Ginger.

If you want to grow your own ginger just buy some roots at the grocery store and keep them moist and warm and they usually sprout. Plant them in a pot during the winter and use them as a house plant then put them in the ground (on the surface, not buried deep) in the late spring. By late summer you will have all the ginger you'd ever want.