Purists hold that the "contemporary" bike era began in 1983/4 with the advent of the first "Click" or indexed components.
For practical purposes though, our Contemporary bikes are basically anything issued in the last 10-15 years, and primarily since 2000. They have shifters on the handlebars (STI in Shimano-speak, Ergopower in lingua Campagnolo.)
In terms of frame materials they could be made of all carbon frames (the most recent, lightest and most expensive), aluminum (slightly less recent, slightly less light and slightly less expensive than carbon) or a combination of the two.
Vintage and Classics bikes basically date from the 1980s or earlier. Most of the frames are made of steel and were hand-made in small workshops in France and Italy. This is the true artisan era of cycling. Riding a classic like this is like driving a TR6 or a Spitfire or a Fiat Spider as opposed to a... Porsche Boxster or a Mazda Miata.
Fans of classic steel frames (and I am unabashedly one -- ALL my bikes are steel framed) identify their worth (the frames that is, not the cyclists) by their frame stickers. The stickers indicate who made the steel tubes and how high quality they are.
Quality in tubes is usually measured by thickness of the tubes and by the overall weight of a "tube set" (all the bits of steel tubing -- typically 11 pieces -- required to make a frame.) A tubing manufacturer might offer a dozen different grades of tubing which they label differently (as in beef grading with AAA, Prime, Angus, etc.)