It is in the listing / testing requirements. "Relays" are intended for "Pilot Duty", meaning they are not expected to switch loads with high inrush and/or low power factor. "Contactors" are, plus contactors have a higher expectation of over load capacity. Relays on the other had are expected to be capable of a much higher duty cycle than contactors, and a typical relay electrical life span for the contacts is 10 million operations, where a contactor would be 1 million. So it's a trade off.
In contactors, the difference between a lighting contactor and a motor contactor is mostly just the ratings of the contacts; the same set of contacts will show a higher amp rating in a lighting contactor than in a motor contactor. So you can always use a motor contactor for lighting, but not the other way around unless you derate it, and unless the mfr shows the motor switching rating, you have no way of knowing by how much. There are also latching contactors for lighting, something you would never do for motors and with some electrically held lighting contactors, the coils are made to be extra quiet in case they are mounted in a living space. You don't want coil hum to be amplified by walls. That makes the coils a little more expensive to make. Because motor contactors are usually controlling noisy machines anyway, nobody worries about that.
"Dear future generations: Please accept our apologies. We were rolling drunk on petroleum."
— Kilgore Trout (via Kurt Vonnegut)