Some USB-C cables marked with Thunderbolt icons were tested to work with USB at all speeds, exceptions will be cables over one meter long that are optical cables or with signal amplifiers. Some cables with USB-C connectors not marked with the Thunderbolt icon will work as a Thunderbolt cable. I don't know if there's any real change made to the cable spec from 3 to 4 but those tested to the Thunderbolt 4 spec will have a small number 4. Like with USB there's often a small number next to the icon, this does not indicate speed but version.

Thunderbolt 3 and 4 is a superset of the USB specification and so USB-C cables with the Thunderbolt markings will work with USB devices. Thunderbolt 3 and Thunderbolt 4 use the USB-C connector but will not always have the USB markings on the cables and ports. Getting a bit off topic is the matter of Thunderbolt cables. Making cheap cables and putting trademarked icons on them without permission is illegal so they tend to disappear shortly after they appear. Making cheap cables is not illegal so there are plenty of those.

To get one of these would mean someone is really digging for a bargain or got very unlucky with an imitation making it to a reputable retailer. There's other answers that will point out that there are cheap imitations that have the USB trademarked icons but these are quite rare. Testing these unmarked cables by plugging them into a computer can do damage so buyer beware. These will be cheap imitations and since they don't adhere to the specified marking standard there's no telling what the cable is capable of doing without testing it. There are cables that will work for USB but lack the USB markings.

Examples of these icons, old and new, can be seen on the USB4 Wikipedia page: Newer USB4 cables will have a large 20 or 40 with the trident instead of the SS, but I have not seen this yet on any products. The number indicates tested bandwidth in Gbps, and having no number means it was tested at 5 Gbps. USB 3.x cables will have the trident with the additional stylized 'SS' on the trident and often a small number 5, 10, or 20. USB 1.1 and 2.0 cables will have the original USB 'trident' icon. Cables that adhere to the USB spec are required to indicate the USB version and data rate the cable was tested to meet.

Usb 2 vs usb 3 picture quality