I have not found a convincing history of white-stem burley. The other grouping is called "red burley", though I cannot tell you what varieties those might be. My guess is that during the 19th century, burleys that color-cured most easily were casually selected by growers. Due to a lack of any understanding of genetics, the truly distinctive "white" burley gradually began to lose its apparently recessive chlorophyll mutation.
Here is all the information I've found:
VARIETIES OF TOBACCO GROWN.
The White Burley, the only variety grown to any extent, is of medium size, the leaves usually attaining a length of about 24 inches, sometimes, however, on heavily-manured lots, reaching a length of 42 inches. It has generally in growing cream -colored leaves, but these run into various shades of green ; so that a field shows a great variety of colors, from a milky white to a deep sea-green.
The Red Burley, which produces a greater number of pounds to a given area, is planted to some extent; but the quality is not so fine, nor does it command such ready sale as the white variety.
The White Burley is losing some of its distinctive features. At first the stalk and leaves were white, but each successive year shows a larger proportion of green. The original White Burley, when cured, had a golden surface, but this golden color is giving place to a yellowish -brown or red, and each successive crop shows a nearer approach to the Red Burley.
Killebrew, JB. REPORT ON THE CULTURE AND CURING OF TOBACCO IN THE UNITED STATES. Govt. Printing Office, Washington, DC (1884).
You can find this informative book in various formats at archive.org, along with Killebrew's second book (1898).
Bob