Although they are not the same thing there are large areas of overlap between them. I’ll assume you already know what frugality is. Simple living or voluntary simplicity as it is also called has many different definitions. To me it means using a minimum of products and services. Others have a different idea of what simple living means. If you visit SimpleLiving.net you can read how others define it and find hundreds of resources on simple living.
If you are living simply you are most likely living frugally. By minimizing the products and service you consume you are spending less money. The savings are ongoing because having fewer things means fewer maintenance costs. On the flip side if you are living frugally there is a good chance you are living simply. Many frugal people are probably practicing voluntary simplicity without realizing it.
I want to emphasize that simple living is not the same as living like a monk. (Although that is a valid form of simple living if it is your preference.) Although I live simply I do spend money on more than just the basic necessities. I will spend my money to see a movie, travel, or on other things that aren’t necessary. It is just that when I do so I make a conscious decision that the money spent on the activity is worth the money being spent. Also I do these activities rarely enough that when I do do them they are a special treat. I could do better and am trying to do so but I think that I am mostly living in accordance with my values.
Simple living doesn’t mean a reduction in quality of life. I think it leads to a better quality of life. Having fewer things means fewer things to worry about. That peace of mind is worth a lot to me. Everyone is free to live their own lifestyle but I think that if more people would choose to live simply it would raise everyone’s quality of life.