In modern PAS parlance we have a Drag Paradiddle #1 and a Drag Paradiddle #2. These are similar but the #2 is longer, with an extra Drag added to the notes of the #1. These two Drag Paradiddle variations have been the most often used since about World War II, but they are far from the ONLY Drag Paradiddle variations to be used in the USA or elsewhere. Check out the pdf for notated examples.
Ashworth used some Stroke and Drag Paradiddles in his music in 1812, but did not name them. Rumrille and Holton also included a similar figure in 1817, again with no name.
The first named Drag Paradiddle I have been able to locate was listed in British Drum Major Samuel Potter’s 1817 Art of Beating the Drum. In fact, Potter listed three different variations: Drag Paradiddle, Stroke and Drag Paradiddle, and Flam and Drag Paradiddle. The second one, Stroke and Drag Paradiddle, is what we now call Drag Paradiddle #1. Potter’s Drag Paradiddle was actually shorter, without the initial Single Stroke. It is uncommon to see a Drag Paradiddle without the “Stroke” in modern music, and both the PAS and NARD rudiment sheets ignore this obvious and simple variation. The Flam and Drag Paradiddle simply placed a grace note before the “Stroke” of the Stroke and Drag Paradiddle (Drag Paradiddle #1). So, essentially, Potter had a Single Paradiddle with a pair of grace notes on it (Drag Paradiddle), a Drag Paradiddle with a Single Stroke in the front (Stroke and Drag Paradiddle), and a Paradiddle with a Flam in the front (Flam, and Drag Paradiddle).
G. Tamplini furthered the British mastery over the Drag Paradiddle in around 1850-1860. He published two more variations: the Stroke and Single Drag Flam Paradiddle and the Stroke and Double Drag Paradiddle. Of these, the notable one is the latter, which is essentially the Drag Paradiddle #2.
Americans did not name any Drag Paradiddles until 1862 when H.C. Hart and George Bruce (Barrett) published three versions between their two books. Hart called his the Paradiddle Drag Beat (Drag Paradiddle #1) and Bruce (Barrett) had two, both simply called Drag Paradiddles. One was similar to the Drag Paradiddle #2, but without the initial Single Stroke, and the other had three Drags before the Paradiddle, like a “Drag Paradiddle #3.”
The actual Drag Paradiddle #1 and Drag Paradiddle #2 naming conventions made their official American debut with Gardiner Strube in 1869. He renamed Hart’s Paradiddle Drag Beat and Potter’s Stroke and Drag Paradiddle to the familiar Drag Paradiddle #1 and he pulled in the Stroke and Double Drag Paradiddle from the British and renamed it the Drag Paradiddle #2.
Many Americans, such as John Philip Sousa in 1886, used the Drag Paradiddle and Stroke and Drag Paradiddle names from Potter and other British sources, while ignoring Strube’s numbered names. The #1 and #2 wouldn’t catch on widely until the 1930’s when George Lawrence Stone, and eventually NARD, started promoting Strube again. Only in the 1950s and later would the Strube/Stone/NARD #1 and #2 names (and actually the #2 rhythm) be nearly universally accepted.
The Drag Paradiddle (sans stroke) has not died out entirely, but is fairly rare in American playing today. The other variations above are almost entirely unknown. One of the last books to catalog some of the older iterations was Vincent Mott’s Evolution in 1956.
Pipe band drumming is really the only other world rudimental tradition to embrace the Drag Paradiddle. It appears in drum settings from as far back as 1919, and may have been used earlier. Pipe Band drum settings weren’t normally written down in notation prior to the early 20th century, so it is hard to know. The Scottish version is like Potter’s Drag Paradiddle (sans stroke) but the grace notes can actually be placed on different parts of the Paradiddle, creating a few variations.
Outside of the UK and USA, the concept is pretty much absent. The French, Swiss, and Danes are known to use Paradiddles in their traditional playing, but none have a named Drag-Paradiddle-like rudiment. It seems to be confined to the Americans, British, and Scottish. The concept is clearly well-liked with more than seven unique versions in print, even before the rise of corps-style hybrids.