Older Thunderbolt 1/2 ports on older Macs can only handle the Thunderbolt protocol while the USB-A ports can only handle the USB protocol.
Only the newer 2016+ USB-C Macs have a combination Thunderbolt3/USB3 ports (some may have Thunderbolt4/USB4) which support both the Thunderbolt protocol and the USB protocol.
USB-C is not a protocol, but a connector type which can support Thunderbolt protocol and/or the USB protocol. The device itself will determine which protocol(s) are available. It is very unfortunate they chose such a name for a connector type as is confuses everyone.
You need to determine which protocol your external device is using in order to know which port to use on the older Mac (including the adapter you need to use). If your external device has a lightning bolt icon next to the USB-C port, then it indicates it supports the Thunderbolt protocol. If there is a USB symbol next to the USB-C port, then it indicates the port supports the USB protocol. You can also check the user guide for your device to determine which protocol(s) the device supports.
If I had to guess the majority of devices with USB-C ports will most likely be using the USB protocol, but you need to confirm it to be sure.