Yep, classical rating exists since the beginning of professional chess. Though with passage of time it was getting less interested for people to follow games for 2-3 days. It triggered the emregence of rapid time format to keep the sport interested.
When asked about elo, it is expected that player would mention their rapid be it any time format in rapid segment
If somebody says they're a 1300, is it generally safe to assume that they're talking about their 30 minute rapid rating? Or would they be talking about their blitz rating?
I'm a 1159 in Rapid but a 859 in blitz. Could I consider myself a 1159 in chess without feeling like a fraud?