In drumming terminology a roll is a long tone, played by hitting the instrument multiple times for the duration of the written note— or for the intended duration of the note, if we're talking about an improvised or non-notated part. It's supposed to sound like a long tone, not a rhythm; the texture may vary, but to be called a roll it has to be perceived as a long tone.
In some older, rudimental usage I get the impression that it's intended to mean any steady rhythm at all using a hand-to-hand motion. That's an archaic usage, and I consider it wrong today.
Played with alternating strokes, one note per hand. The standard way to roll on cymbals, timpani, concert bass drum, mallet instruments, woodblock, and other percussion instruments. On percussion instruments it must be played fast enough for the resonance of the instrument to blend the individual strokes together to make a long tone; so more resonant instruments like concert bass drum, larger timpani, suspended cymbal or vibraphone may call for a slower roll speed, and drier sounding instruments like wood block, xylophone, or smaller timpani will call for a faster roll speed. On drumset the term is generally used to mean fast alternating strokes on the drums, without the strokes necessarily blending together.
Also called a double-stroke roll, it's played with alternating strokes, two notes per hand. Machine gun-like, standard for rudimental drumming, and modern drumset for soloing, filling, hihat embellishments, and brushes.
Also called a multiple-bounce roll, orchestral roll, or buzz roll. Played with alternating strokes, with multiple notes per hand, overlapping to make a continuous tone. Smooth-textured, standard for concert snare drum in all settings, and on drumset.
This meanings of open and closed are different from what they were in the past; traditionally they seem to have meant slow and fast— I believe that's a reflection of how military drumming was taught in the 19th century; it's archaic and has little to do with current musical reality.
The so-called “one handed” roll is really a drumming trick, and doesn't have any standard musical application on the snare drum or drum set; it's strictly for show. Some percussion instruments may use a one handed roll played by alternating between two surfaces of the instrument, like in the corner of a triangle or the mouth of a cowbell; there is a similar one-handed brush technique for snare drum using a rapid back-and-forth motion— functionally that is a roll, though I never hear it called that. Cymbal rolls can be attempted one-handed with a mallet if the other hand is occupied.
Three-stroke rolls are a type of open roll with alternating strokes, three notes per hand, usually in a sixtuplet rhythm. Strictly a modern rudimental thing, and not normally used in any other playing; drumset players with drum corps background sometimes use it in soloing as a sort of technical display. I find it to be musically uninteresting and useless.
Construction and notation
Ties, releases, taps, and accents
Usually a roll consists of the roll note itself, tied to a single note release. Rolls written without a tie end without a release, with a little space between the body of the roll and the following note. In Stick Control, George Stone presents untied rolls as ending with an unaccented tap before the next written note (exercises 13-24 on pages 11 and 12 illustrate this). Often rudimental rolls will start with an accented tap at the beginning. Orchestral rolls written with an accent, a fp, or an sfz will have the first, or first two, multiple-bounce strokes accented. In soloing on the drumset, some players will accent multiple-bounce strokes during the body of the roll.
There are two rhythm components of any roll: the written (or intended) duration of the roll itself, and the pulsation speed— the rate of hand motion— to make the roll. The rate of pulsation is determined by the tempo of the piece, and the instrument on which the roll is being performed; it has to be fast enough to make a smooth long tone on that instrument. Often it's assumed to be 16th notes, but depending on the tempo it may be sixtuplets, 8th note triplets, 8th notes, 32nd notes, quintuplets, or septuplets. Pages 38-46 in Stick Control are designed for developing rolls at different tempos, with different pulsation rates.
The current American standard notation assumes all rolls are 32nd notes. It's beyond the scope of this post to explain it in detail, but that's what those familiar roll-indicating slashes connote. Three slashes are used with whole, half and quarter note duration rolls; two slashes are used on 8th note duration rolls, and a single slash is used for single 16th note drags. The three slashes— or one beam + two slashes, or two beams + one slash— indicate the three beams used in notating 32nd notes. They're an abbreviation saying “play this note value for the duration of the note the slashes are adorning.”
It's bastard notation, because if the roll were literally played as 32nd notes, it would not be necessary to have a tie. The only time rolls are actually meant to be played as 32nd notes is when they're in open, rudimental form— but the tie is still used in that setting. Otherwise, what is meant by the notation is to play as many roll strokes as are needed to make the roll sound like a long tone.
A European convention is to notate rolls as a tremolo, with or without ties as in standard American notation.
Note: the PAS graphic at the top of the page distinguishes open rolls from buzz rolls by using the slash notation for open, and an italic Z for buzz; this is not standard throughout the drumming literature. The only place I've seen that to be the case is in marching percussion. In most standard literature, the slash or tremolo notation is used, and as a performer you are expected to know the right kind of roll to use for that setting— almost always either multiple-bounce, or single stroke, again, depending on the instrument.
A drag is a single double stroke or multiple-bounce stroke. It can be a component of a ruff, or it can be played by itself in the middle of a run of notes— typically 16th notes or triplets, typically in a rudimental or drumset setting. There is also a specific rudiment called a drag, the definition of which actually varies, depending on who you talk to— I'm using it generically, not attached to a specific pattern.
There are probably a number of rudimental people who would use this term only in association with the actual formal rudimental pattern, who would consider my definition above to be wrong. But that was a common usage of the word by the corps people I learned from, who were all in the 70s-80s Santa Clara Vanguard orbit— SCV instructors, or former members who became instructors.
Technically not a roll, but it's in the roll family. In modern usage it's a short, unmetered, multiple-bounce stroke adorning a tap; or three unmetered single-stroke grace notes adorning a tap. There is some contention online about ruff terminology, and how they're executed, but I have no interest in that. Again, I learned this from Charles Dowd, who learned it from Tony Cirone and Saul Goodman, and that to me is authoritative.
Rolls with the familiar names 5, 7, 9, 11, 13, 15, and 17-stroke. The names refer to a hand motion, counted as two notes per roll stroke plus one note for the release. With multiple bounce rolls, the name will not reflect the actual number of notes played: an orchestral 5 stroke roll is played with two multiple bounce strokes and a release, so you're not literally playing five notes.
There are also 6, 8, and 10 stroke rolls that typically have two taps: at the beginning and end, or both at the beginning or end. The terminology is not perfectly scientific, because there are versions of the odd number-named rolls that start with a tap and end with a tap, yet both taps are not counted in the name of those rolls. It may have to do with how they were used in traditional rudimental drumming— rudiments were not just patterns in the abstract, they were formalized pieces of verbatim musical content.
For what it's worth, the only numbered terms I personally ever use are 5, 6, 7, and 9. For longer rolls than that, I think of them only in terms of their duration and pulsation rate.
A long roll is any roll longer than the ones for which we have numbered names.
So, that's a fairly exhaustive overview of my roll knowledge, at least as far as verbal information is concerned. Some people's textbook definitions will certainly differ from mine. For further study, I'll write a roll studies bibliography and post it another time.