Have a look at the processor - the Mac Classic uses a 16 Mhz 68000, whereas the Classic II uses a 68030. Alternatively, try holding down Command-Option-X-O at startup. If it is a Classic, it will start up off an internal ROM disk, rather than the hard disk or floppy. If its a Classic II, it won't.

It sounds to me like you've got a Classic with a Classic II front - a Classic II has onboard RAM slots, and does not take the Classic RAM expansion card, the slot that it has is physically identical, but is for an FPU or ROM upgrade, I doubt that the Classic RAM expansion card would be electrically compatible.