That's right. An SE/30 and Classic II are 68030 Macs. 68000 Compacts don't do the chimes of death.
The Classic is a glorified SE/FDHD. It uses the exact same ROM except for some modified code for the Classic's software screen brightness and the built-in ROM startup RAM disk. If you have heard a stock Classic make the chimes of death, then it is unknown to me. My Classic does not make it, though otherwise works perfectly. Most likely you have seen a Classic which has been upgraded to a Classic II.