I just received a firewire to thunderbolt adaptor. It does not fit the thunderbolt port on my new iMac.

You also need a Thunderbolt 3 (USB-C) to Thunderbolt 2 adapter to plug that Thunderbolt 2 to FireWire adapter into.

Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple

The Mac's external ports have changed every couple of years.

The first TB 2 to FireWire adapter you bough, works with the previous TB 2 Mac models.

It is unfortunate, but you need both adapters to connect an external FireWire drive to any of the latest TB 3 (USB-C) Mac's.