Brown rice is the rice that's obtained when the husk is removed. It's the most intact grain with just the indigestible husk discarded. The picture above (image courtesy) shows Rice husks, the outer covering of rice that's removed using a process called Winnowing where wind is used to blow away the husks from the rice. No other processing is done to the rice thereby keeping both the bran and germ intact hence most nutritious.

Hand pound Rice (kai kuthal arisi in Tamil), on the other hand is a rice whose husk has been removed by using a stone grinder or a stone apparatus similar to a mortar and pestle. The picture below (image courtesy) shows women pounding the rice using hands (hence the name) that helps to seperate the rice from the husk. In this process there is some breakage due to manual pounding and some bran gets removed as well. It is minimally polished (low glycemic index, similar to brown rice) but still retains most of its nutrients. In short, Hand Pound rice is right in the middle of White rice (fully polished) and Brown rice with white rice (high glycemic index) being the least in the nutritional profile.

In short, if eating Brown rice does not appeal to your senses, or if you are just starting the elimination of white rice from your diet, you can start with Hand pound rice. In the US, I find hand pound rice readily available at my local Indian grocery stores by the same name. In your location, you might find a different brand. If unsure, ask the store person for hand pound rice.