Vintage is something old.

A classic is a statement and is timeless.

Interesting thread, I at one time owned five Treks from '79 to '87, I considered them classics because of their lugged steel frames. I am now down to the '85 and '87, both updated to STI. I still consider them as classics.
In the history of Trek they may be considered vintage.
IMHO

"Classic" means almost old enough to be an antique; "vintage" means just old enough that you can't find the right parts to fix it.

Or to put it another way, "classic" is old enough for sclerosis; "vintage" is finally old enough to drink.

I think "Classic" is a function of three things: time, attrition, and desirability.

in the automotive realm there were hundreds of thousands, if not millions of '57 Chevys and '65 Mustangs built. I'm old enough to remember when they were pretty common and were merely "used cars" for a while. With time, most of them were reincarnated as refrigerators or backhoe buckets- and may yet exist today as Chinese Walmart steel bikes! They got wrecked, rusted away, quit running, etc. and just vanished. Yet, so many were fond of them later they began to be sought out- as many had desired them when new. Not to mention later generations came to want them as well. So it got to the point where excellent examples were expensive, and with some variants it was even worthwhile to nearly reconstruct a derelict example. Time passed, numbers shrank, and demand came back (or never left)- time, attrition, and desirability. Remember old Henry made 15 million Model T's and a lot of folks still lust after one.

Even though many may not think the Schwinn Varsinental the greatest bicycle produced (and let's face it, it wasn't) and millions went out the door, Schwinn ain't making them in Chicago anymore with EF frames. They made a gaziilon of them, so we know they were pretty popular, desirable. The numbers are dwindling as most meet the fate of the the previously mentioned cars as time passed. But a lot of boomers want one to take on the village bike path and plenty of hipsters and other urban types like their cachet (yes they have that) as well as there durability and simplicity- they are in demand. Indeed, those three original factors make them classics. And one day they will no longer be found languishing in garages, or rusting away under a deck- and they will still be wanted...

The Varsinental is an admitted entry level notion as to what makes a classic, but its pretty valid. In varying degrees and balance time, attrition, and desirability play a role with many other bikes. Performance, equipment, and exotica can all play a role in desirability. Maybe a Paramount is a sort of Gullwing Mercedes?

Time in the form of age is the chief factor in "Vintage". I don't know how many are drooling over a wood rimmed Safety Bicycle or a Wright Cycle Company Van Cleve- but I bet many more would over a Miyata or a Raleigh DL-1. But the former pair are definitely "vintage", at least more so that the latter pair.

However I'll suggest a new category- Veteran. In Britain auto buffs use "Veteran" for horseless carriages and "Brass Cars". Maybe "Veteran" could be adopted for bicycles made before the end of WW I- before the US market tilted so much toward children? Just a thought...