Yes, the C/K 2500/3500 trucks were made until 2000, but those were not referred to as "classic," that I'm aware of. Simply C2500, C3500, K2500, K3500. They also dropped the "Silverado" trim, I think in 1999, when the GMT 800 "Silverado" came out...Confused yet? The previous Silverado trim on the GMT 400 got replaced with "LS" on the little cab sticker.
The "3500HD", (19.5" rims, heavy beasts) technically also a GMT400, were made until 2002.
I have a 2000 K3500 LS CCLB SRW (GMT 400) and a 1999 Silverado 1500 ECSB LS 2wd (NBS, GMT800). I always have to explain to my son, who is 9, why the "newer" truck looks older than the "older" truck, LOL.
I think some of the confusion comes from folks calling their trucks "Silverado" instead of C/K____ at the parts counter. And it probably doesn't help that the guys behind the counter can't tell one from the other on their screens. Every website on parts that I've come across is spot on if you know this difference. These transitions years for GM trucks are always confusing, as new body trucks roll out and the older generation of trucks are still being made simultaneously. Trim and name changes doesn't help, LOL.
Example: Going into the parts store and telling the counter guy you need a starter for a "1999 Silverado 2500", when your truck is a "1999 C2500" (Silverado-trim?) is guaranteed you will get the wrong part.
At least GM never made a 7 lug truck like Ford F-250!