Here’s hoping/assuming I define these things the same way your book and everybody else does.
A riff is a repeated motif used in a song, usually the guitar but it could also be the bass or keyboards. Think Stevie Wonder in Superstition. This is also called the “hook,” and it’s usually the most recognizable musical element in any given pop song.
By my definition, a lick is a non-repeated run on the guitar or bass. If you repeat a lick, it’s a riff - there’s no real difference in what they are, it’s just how they’re used. It’d call the intro to Layla a riff, but if it were only played at the beginning of the song, it would be a lick.
Groove is hard to define. It’s built around the bass and drums and carries the song, rhythmically. It’s what you dance to.
A good example of licks are in the bridge of Heart’s “Magic Man”, right after the brief silence. Roger Fisher (?) reels off a few memorable solo licks in a row before the synth kicks in. Those licks are played at no other point in the song.
Van Halen’s "Jamie’s Cryin’ " is a good example of a hard-rock song that pushes the “groove” way to the forefront. Alex Van Halen’s drum rolls and hi-hat taps are the most notable parts of the song – on this track, Eddie is just their for flavor.
The groove is a repeated rhythmic phrase the rest of a song is laid over. Many songs start with the band members improvising until they have a solid rhythm line going. Then somebody finds a melody and/or words that fit. Sometimes, the lyrics at that point are scat-singing or thrown-together “garbage” lyrics to temporarily fit the melody. Yesterday originally went, “Scrambled eggs/ Oh, my baby, I just love your legs.”
Sometimes, it starts with a riff, or vamp. The guys who wrote New York, New York had to write one more song for a show, on a short deadline. One of them played played that unforgettable opening vamp, and everything else fell into place in a short time.
I think that Marley23, bordelond and AskNott have pretty well covered what I think of when I hear these terms. For further examples, Jimmy Page was the king of riffs in his Led Zeppelin days. So many of their songs were based on cool, memorable, repeated guitar phrases. A great example of what I think of as licks would be the three man solo in The End by the Beatles, in which McCartney, Harrison and Lennon take turns playing licks in succession, three each, for a total of nine licks.
The definitions of the terms varies from musician to musician, but I basically agree with the above, with the caveat that a riff can be a hook, but quite often, for me at any rate, a hook is a much broader term, and is quite often in the vocal melody.
A “lick” for me is something that is used in improvisatory soloing. While these kinds of solos are extemporaneous, musicians build up a personal library of relatively short note and rhythm patterns, which can be connected together while improvising to help glue a solo together, transition from one part to the next, and that sort of thing. These are “licks,” although I have heard guitars refer to these as “riffs” as well, as in “check out this cool new blues riff I learned.” For me, a riff is a short, repeated pattern which often forms the basis of a song. Think Led Zeppelin and the guitar in “Whole Lotta Love” for example, for an example of a quintessential riff. For that matter, take almost any Zep song for riffage examples.
However, in practice, “riff” and “lick” can be used somewhat interchangeably, although I usually hear “riff” used in places I would use “lick,” but not the other way around.
edit: I see Crotalus beat me to the Zeppelin example. Zeppelin is also a great example for groove. “When the Levee Breaks” starts with a great, rhythmic groove.
A riff can be a hook, as you say, but a hook doesn’t have to be a riff. I was just listening to **Just Can’t Get Enough by Depeche Mode ** and was stunned by how hooky it was. There are at least 3 synth hooks - each clearly distinguishible yet woven on top of each other - and a couple of vocal hooks going on at once. A hook is any short, memorable musical phrase that easily gets stuck in your ear - that song is full of them.
To me, a riff is repeated, yes, but is usually not something that could be confused with a lead line. So **Smoke on the Water ** is a riff, but (again, to me) **Layla **isn’t a riff because it is a lead line used in a riffy sort of way. This is pretty idiosyncratic, so no need to disagree - this is all IMHO - but I find when I do compare notes with other guitarists they tend to think this way too…we tend to think of Satisfaction, Sunshine of your Love, Back in Black, etc. - as riffs…
A lick is a cool lead line that you want to add to your arsenal. Chuck Berry’s intro to Johnny B. Goode (or Roll Over Beethoven, or Carol, or…) is a great example of a lick.
A groove is about whether the rhythm makes you want to move. A song has a groove typically if the rhythm is influenced by r&b, jazz and blues - where the drums play “behind the beat” - which I could play for you but is harder to describe; it basically means that the drummer is not playing metronomically “on beat” like, say a military drummer (or Lars Ulrich of Metallica 99% of the time) but instead putting pauses in the drum phrasing, waiting until the last possible second before hitting one beat, then hitting the next one on time - anything to make the beat feel propulsive, not boring and predictable. Funk music - e.g., James Brown, Parliament/Funkadelic, the Isleys, a lot of Prince, etc. - are defined by their groove…
ETA: ah, a few other musical-regular Dopers have weighed in on the Riff vs. Lick issue as I tried to do…