Connecting an old 27" Apple Thunderbolt Display to a MacMini M2

I have a 27" A1407 Apple Thunderbolt Display (specifications Apple Thunderbolt Display - Technical Specifications (UK)) currently connected to a MacBook Pro Retina 2014 via A Thunderbolt 1 cable. I want to buy a Mac Mini M2 but I need to know how to connect it to my Display. I have seen answers saying they're compatible with this adapter Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple But my (sorry if naive question) is: "Does this Thunderbolt 2 Adapter also work on Thunderbolt 1 ports"? They look slighty different to me (Thunderbolt 1 being more rectangular and 2 being a bit curved).

Thanks