It seems that the term is used differently in UK from in US. I think
@flowerbug is right in suggesting a connection with size but in Britain the term seems historically to be used for this kind of bi-coloured bean whereas in US it is more likely to be used for navy beans, ie. small white beans.
The AI answer is:
The term “pea bean” originally referred to several varieties of beans that resemble peas in size and shape. In Britain, “pea bean” was used to describe a bicoloured climbing bean—typically Phaseolus vulgaris, recorded since the 16th century—whose small, rounded seeds could be eaten in the pod or as mature dried beans. In the United States, the same term came to describe small, white common beans, especially the navy bean, which fed sailors in the 19th century and became synonymous with the name “pea bean” or “white pea bean”.