I am no expert, but...
When I was a kid, rode 20 x 1 7/8. (Discovered relatively late in
childhood that pumping them up *really* made it easier to get going
faster.)
As a teenager, finally got on 26 x 1 3/8 tires, and then even rode a
10-speed w/ 27 x 1 1/8 - this latter is what I would call "skinny
tires", and they seemed faster than bigger diameter tires (and had a
higher rated pressure specification on the side, so... )
When I started riding (more) again in early adulthood, I had a sweet
(brand spanking new) entry-level Miyata w/ 27 x ~1 1/8 (?) That bike
was awesomely springy yet just right tight, and pumped up to spec
seemed to have low rolling resistance (went fast).
When I started riding again in later adulthood I had a Trek 400 from
same era as the Miyata, similar bike w/ similarly sporty feel - 700C x
28 mm tires - I would still call these "skinny tires".
Then I got the Surly LHT that came stock w/ 35 or 37 mm tires (don't
remember exact spec, btu they were *not* skinny tires. Bouncier, but
not really plush (Conti Contact Sport) - kind of stiffish. I replaced
these w/ Vittoria Randonneur Pro 32 mm (had run Randonneur 28's on the
Trek) - ahhhhh... great balance of bounce and tighter and responsive
and plush.
Oh... meanwhile I ahd gotten the '89 Miyata 914 (the bike I could
never afford when new) w/ 23 mm tires. These were definitely "skinny
tires" - almost felt like riding on a rim strip or something (they
were pretty nice Vittoria Rubino Pro road tires).
*Anyway*... I categorize 28's as skinny tires, and 32's as not skinny
tires - more "versatile" (I tend to got off road about every chance I
get). I had to sell the 914 :-(, but my plan for it was to try 25 mm
Vittoria Diamantes, which I think would have been perfect.