Great question! Thunderbolt is confusing because it is often confused with Apple's Lightning protocol that is proprietary to their devices (iPhone/iPad). Thunderbolt 3 is identical to USB-C physically, but it supports up to 40Gpbs transfer rate, whereas USB-C is only up to 20Gpbs. To make matters worse, devices don't always have the Thunderbolt icon next to their USB ports that support that protocol so you might have to check documentation to make sure. The laptop I use has 3 USB-C ports, but 2 of them on the rear of the laptop are marked as Thunderbolt so I know it is supported. I believe MacBook Pros don't mark them at all because all of them support that protocol.
Thunderbolt is backwards compatible with USB-C, so if you're planning on upgrading your laptop in the next year or two anyway it can be a good idea to get the faster device now. It also makes it less likely of having an compatibility issue when sharing the drive with someone else.
Since the cables may or may not have the Thunderbolt icon on them, you also need to make sure you have the appropriate cable (most, if not all come with one these days). Again, if you only have a USB-C cable for your Thunderbolt SSD, it will most likely still work fine, it will just be at that slower protocol. Hope this helps.