"They" aren't really correct. USB-C and USB-A are plug/connector types (as is USB-B and the various mini and micro versions of -A and -B), not transfer protocols. Transfer speeds are determined by the USB standard, e.g. USB 1.1, USB 2.0, USB 3.0, USB 3.1, etc.
USB-A connectors can be 1.0 and up, USB-C connectors can be USB 2.0 and up but are generally USB 3.0 or 3.1. Thunderbolt 3 is equivalent to USB 4.0 and uses the same physical plug as USB-C.
Max speeds are:
- USB 1.1 - 12 Mbps
- USB 2.0 - 480 Mbps
- USB 3.0 - 5 Gbps (~10x faster than USB 2.0)
- USB 3.1 - 10 Gbps
- TB3 - 40 Gbps
For USB-A ports, you can tell the standard by the color of the plastic bar in the port – white is USB 1, black is USB 2, and blue is USB 3 (but you'd need to look at the drive specs to see if it is USB 3.0 or 3.1).
So, if your drive has a blue USB-A port you can get 5 or 10 Gbps max speed, if it's black you can only get 480 Mbps max speed.
However, if your external drive is a regular HDD (with a magnetic disk inside spinning at 5400 or 7200 rpm), the average data transfer speed off the drive is ~800 Mbps for 5400 rpm and 1.2 Gbps for 7200 rpm. Thus, if your drive is USB 3 the limiting factor is the drive itself, not the USB connection.