Are soap nuts nuts?

Sofie, a French lady from our compound, showed me around the 'neighbourhood' yesterday. We went to 100 feet road and 80 feet road in Indiranagar. Our compound is in Basavanagar, India likes long names ;-).

The driver dropped us of at the beginning of 100 feet road and we walked all the way down, had lunch and walked back along the other side of the street. 80 ft road was done by car, because we were too tired and warm. It was a great day.

At one of the side streets is a fantastic shop called The Ants, Crafting traditions. They sell only products from India, from fabrics to pottery and furniture. But they also sell soap nuts. I had never heard of it, but Sofie has been using them for years already and used to buy them in France. Strangely enough they are hard to find in India. According to the leaflet "soap nuts, or Reetha, are actually not nuts. They are the fruit of the soap nut tree which are harvested and then air dried". The soap nut tree grows in the Himalayas.
I have bought 2 packs, one for my mother in law who is a real 'natural type' and one for myself, because I want to see if it really works. As I am writing this my first load of washing with nuts is in the machine so I will know in about an hour if is a good alternative to washing powder. So soap nuts are not really nuts, but am I nuts for using them? I will keep you posted!