These conductor classes are specified under EN IEC 60228. Note the industry term "Class 3" officially means Class 5 flexible conductor, with no formal Class 3 standard.
Class 1 cable
It has one solid single copper core, completely unstranded. Hard and stiff, cannot bend frequently. Typical model: H07V-U, used for fixed concealed wall wiring. Wires break easily with repeated folding.

Class 2 cable
Constructed with several thick copper strands twisted together. Slightly flexible for easy conduit pulling, still designed for stationary installation such as cabinet wiring and YJV power cables. It maintains good structural rigidity.
So-called Class 3 (Class 5) cable
Made of numerous ultra-fine annealed copper strands tightly twisted. Extremely soft, tolerates continuous movement and bending for drag chains and appliance leads (e.g. H05VV-F). Strands will fray without crimp terminals, and its DC resistance is marginally higher.
In short, you can tell them apart by copper structure, softness and applicable usage scenarios.