firewire to thunderbolt 3

I just received a "Thunderbolt to FireWire Adapter" that I bought in the online Apple Store. The firewire end fits my external hard drive just fine, but the "Thunderbolt" end of the adapter will not fit on my brand new iMac. It is too big for the hole on the back of the Mac. What do I use to connect my external hard drive to the Mac? Do I have to buy a whole new external hard drive? Is the thunderbolt on my new Mac different from other thunderbolts? How do I use those tiny holes on the back of the Mac?