As long as I’ve been playing, with the people I’ve been around*, open and closed were understood to refer to, respectively, double-stroke, rudimental-style rolls, and multiple-bounce, orchestral style rolls. Double strokes = open, multiple-bounce = closed. That has been the modern meaning since at least the 1930s, when George L. Stone gave these definitions in the introduction to Stick Control:
The “open roll” referred to through the book is the rudimental roll of two beats (no more) of each stick […].
The “closed roll” […] is the one commonly used in light orchestral playing. It has several rebounds to each stick movement…
Reading the recent collection of Stone’s own published articles, Technique of Percussion, in his day there was debate about the meaning of the terms, and about roll interpretation. Evidently a good number of those older people didn’t even recognize the multiple bounce stroke as a legit thing. It was controversial enough that Stone had to make a case for the multiple-bounce roll and drag— and eventually prevailed, with the definition above.
In some older books open and closed seem to mean simply slow and fast. Rudimental drummers will demonstrate a rudiment “open to closed”, slow to fast. And Stone himself, in an early piece in Technique of Percussion refers to practicing double-stroke rolls “Open to Closed (slow to fast).” Recently we saw in Wilcoxon there are some double stroke rolls indicated as “closed” simply because they’re played with a faster pulsation than another example marked as “open.” On YouTube I occasionally catch rudimental people using the terms that way today.
I normally reserve the term roll for things that are meant to be heard as a long tone, but there’s an antiquated definition that includes any fairly rapid hand-to-hand playing in a steady rhythm. So I use a third category, a rhythm form— which is an open-form roll rudiment played slowly enough to be heard as a rhythm, rather than as a long tone. You’ll see that in Wilcoxon— things identified as a type of roll even when they’re not meant to be played at long tone speed.
There’s enough lingering ambiguity about closed especially, that I’m getting away from using it. Usually I’ll say multiple-bounce, sometimes buzz.
Also see my All About Rolls post from a few years ago.
* – I’ve been around a lot of other Charles Dowd students, and a lot of Tony Cirone students. Dowd was a also student of Cirone, and of Saul Goodman.