I'm afraid I am a little confused as well. "Butter bean" usually refers to a lima, but what you are describing sounds more like a snap bean ("green bean").

"Carolina" (or "Sieva") is a white-seeded pole lima commonly grown in your area. It is highly productive, and even does well for me here.

For possible Southern-adapted snap beans, you might want to take a look at those offered by Bill Best:
Sustainable Mountain Agriculture Center

Or those offered by Southern Exposure:
Southern Exposure Seed Exchange

If you can remember anything specific about the bean - especially the seed color - it would be helpful. When you mentioned string, were referring to support for the vines, or removing the string from the pod ("stringing")? Some older snap beans have strong strings which are removed prior to cooking or canning... and some gardeners prefer their flavor.

I remember vividly. It was rural North Carolina, I am sure my grandparents just called them whatever they thought it was. The string was for support of the running vines. They have flat pods and small green beans when ripe. The seeds were when my grandparents would dry out the pods and both the pods and the beans would turn tan or whiteish.
Thank you for your help.

Still confused. Did you eat the green pods or the shell beans? If you are talking about a shell bean. Baby limas are usually called butterbeans in the south. Carolina/Sieva was for years the most popular pole butterbean. Willow leaf was also grown in the Carolinas.

Well there you go! It was shelled. So, it is a baby Lima!!!! Any particular brand or name I should get now that you have some characteristics?
Thank you again

As both zeedman and I stated, Carolina/Sieva would be your best choice to replicate your grandparents butterbeans. Willow leaf (white) is also a possibility for you region. I now grow Mezcla, which is similar to the Carolina but much more productive.

The picture of the beans are the right size but they were always bright green and the picture of the plant looks condensed. Theirs always ran upward on poles and string about 6 feet high. Not as many leafs but a lot of beans.

These were on 7 ft. poles. Vines reach the op and start back down. All three of the varieties named have massive vines. These are also white beans when full grown, altho immature beans will have a green tint. All the green seeded baby limas that I know are bush . Even then they are more green tinted than bright green. Zeedman has much more experience with limas that I do. Hopefully he may know of a green seeded pole variety.

The only pole variety I know that has green seeds is King of the Garden... and even those are not bright green. Not always green either, I had white seeds from a different vendor. King of the Garden has very large seeds - much larger than any of the varieties already mentioned - so probably not what you are looking for.

Based upon your description of the dry beans, chances are that the limas you remember were bright green because they were harvested immature. One of the heirlooms that I grow (1880's Butterbean) is darker green when immature, but those seeds have reddish-purple stripes when dry.

Thank you everyone for your information. I will give the 1880’s a try.

As far as I know, that variety is not commercially available. I obtained it through SSE, and no one is currently offering it there. My seed is in need of renewal (it is from 2014) but because of my storage conditions, should still have fairly good germination. If you would like to try it, I'd be happy to send you some... just PM your address.

You should try the before mentioned Sieva Carolina Butter Bean

This is a famous butterbean type from the Carolinas/ Virginia area, and is reported to be productive many places. They will be light greenish if you pick them while still green.