imac late 2013 what type of Thunderbolt ports

1 caveat. If your external hard drive is not actually Thunderbolt compliant it will not use the Thunderbolt speeds regardless of what its plugged into. It will use the max speed of whatever connection it has. If it has a USB 3 connection that's the max speed it will use.

I wouldn't waste the money on an external TB drive if the internal storage is no faster than 540MB/s. TB is not going to make it faster. I use a 1 TB Crucial MX500 SSD in an external Vantec USB3.1 Gen 2 enclosure connected to my Late-2013 iMac via USB3.1 Gen 1 cable into the USB 3.0 port. Total cost: $140USD (including enclosure).

It has TB 1.0 ports (10Gbps) and USB 3.0 (5Gbps). Obviously, TB is faster.