Are TB3 cables in any way different than USB-C cables?
The "lightning" does not indicate that it can transmit power - it is actually the Thunderbolt logo indicating that it is a Thunderbolt cable.

All Thunderbolt 3 cables have USB-C connectors. Note that this is just the connector itself - it doesn't mean that the rest of the cable is the same.

Ordinary Thunderbolt 3 cables (i.e. cobber-based) also work as USB-C cables. In this manner they are compatible. You can buy optical Thunderbolt 3 cables (eg. if you want a 50 meter cable) - these are normally not usable as a USB-C cable.

On the other hand any USB-C cable is not Thunderbolt 3 compatible. It might be (as ordinary Thunderbolt 3 cables also work as USB-C cables). In general they are not.

The differences are mainly the design and quality of the cable, and to which standard they have been tested before leaving the factory. For example Thunderbolt 3-cables are generally specced to allow much higher amounts of power delivery than USB-C cables.