For me, Simple Living and Frugal do go hand in hand, because
I include time and quality of life as well as economics in my definitions.
Time and quality of life are more important than money. Can anyone argue that? Living frugally means that you don't have to go along with what you're supposed to do or want or buy - you can focus on what's truly important to you. I think that's the gist of living simply, too.
Our culture is a cluttered one, with all sorts of "experts" telling us how to spend our money, how and where to work, what we want to eat and wear and listen to and creating goals for us. When we learn to turn that off and listen to ourselves, we can have a simple and frugal life.
Now, taking your example of growing and canning being more complicated than running to the store... look a little closer at that. "Running to the store" involves a lot of things. First, you or someone will have had to work to make the money you spend at the store. You will have to have transportation. If you use a car, you have to have bought it at some point... more money. Then you need to be sure it has insurance - not only more money, but the hassle of finding an agent and a company, keeping premiums up to date, etc. Going to the store means you have to navigate traffic, which is not always simple in itself.
Now... let's say you got the green beans from your own garden. You bought or saved the seeds, tilled the soil, planted, weede and watered them. Then you picked them and cooked them.
I know this is an extreme example, but which is simpler?