Sorry I don't have an answer, but I didn't want you standing there all by yourself! I've been trying to find out what you call the type of pea that climbs. I think I would have remembered "pole pea" if I had heard it before!

Well here's my interpretation..... a pole bean is a bean that needs something to climb on 6, 8, 10 or more feet.

To me Runners are Phaseolus coccineus like Scarlet Runners, Insuk's Wang Kong, Sunset etc. they also need something to climb on but there's also some short P. coccineus, not sure if they are classed as bush or half runners.

Half runners, never grown them myself but think of them as something in between a bush and a pole bean, they do better with some support maybe 4 or 5 feet.

I have the bean variety called Salmos Greek Lima, you'd think by it's name it's a lima bean, it's not it's a runner P. coccineus but apparently it's supposed to taste like a lima bean hence the name, confusing isn't it.

I think of peas as either climbing or bush. Hope this helps:).

Annette

Concur: By tradition pole beans are climbing versions of P.vulgaris. The name came from the habit of cutting poles and and staking them. Those grown in cornfields using cornstalks for support were called corn field beans. Same type, but the cornfield beans were more vigorous and competitive, tho not as good for snap beans.
Runner beans are P.coccineus, popular in Europe but most have problems with US climate. They like a damp cool climate and are for the most part heat intolerant.
Half runners are normally P. vulgaris. Short vines That are normally grown as a bush bean but can be staked.

Peas, either Pisum sativum or Phaseolus unguiculata subsp. sesquipedalis don't climb poles well so would seldom use pole to describe them. The climbing versions are usually trellised.
Halfrunner variety Volunteer {{gwi:1024713}}

I have been growing a pink eye, purple hull crowder pea for a couple dozen years. It has been so long, I don't know the specific variety. It is a climber and thrives in the harsh Florida summers. I have extra seed if anyone is interested. I usually grow as a cover crop and don't trellis them. They outcompete just about everything.

Thanks! The more I learn, the less I know! Seems every question I get answered just inspires 2 more. :)