I'm no expert, just an enthusiast:
The Standard has the modern vibrato hardware the Vintage Reissues have the older six hole with the stamped saddles. I like the old style.
IIRC, The 57 has a maple fret board and the '62 has the rosewood. The American Standard has either.
Some of the 62's have smaller frets.
The "Vintage Reissues" have a Nitro Cellulose finish over a polyester sealer. The American Standard has polyester over polyester.
The VR's usually come with a snazzy carry case while the American Standards come with a very nice practical case.
The VR's usually have AlNiCo magnet pickups while the American Standards changed over the years with the fashions. I like the AlNiCos.
Most importantly, the Vintage Reissues have color choices that aren't always included in the American Standard selection. I like colors. :-)
best regards,
mike