It all depends. There is no good answer on if you will notice the speed difference, it just depends.
When it comes to backward compatibility you should not sweat that too much. Apple's USB-C ports with TB3 and USB4 will be backward compatible with USB 3.2, 3.1, 3.0, 2.0, and 1.1. I have not seen a TB3 drive that wasn't backward compatible with USB 3.x excepting those big RAID boxes that have some fancy SATA controller under the hood or something.
I've seen USB-C drives become hit and miss when plugged into some USB-A ports because of a lack of power and/or they can't drop down to USB 2.0 mode. If it's a matter of power then a relatively inexpensive powered USB 3.x hub can fix that. If it's a lack of Thunderbolt or USB 3.x then that is fixable now with a more pricy Thunderbolt hub. I'm experimenting with a TB4 hub on a TB2 host with the intent to get the most out of my USB-C devices, and it's not going as well as I hoped. I'm only getting USB 3.0 speeds when I should be getting TB2 and USB 3.1 speeds. It appears to be a software issue that I need to work out.
When it comes to speeds I'll be imprecise with the naming conventions but y'all should know what I mean.
USB 3.0 = 5 Gbps
USB 3.1 = 10 Gbps
USB 3.2 = 20 Gbps
USB4 = 40 Gbps
TB1 = 10 Gbps
TB2 = 20 Gbps
TB3 = 40 Gbps
Because USB and TB encode the data differently they are not quite one to one, TB is slightly faster. Don't pay as much attention to the external interface as it will be the internal interface on the drive that will tell you how fast the drive is. I recall seeing TB3 drives but one had SAS-4 at 22.5 Gbps internally but the other was SATA Express at 16 Gbps.
There's the host controller, the drive, the drive container with it's interface adapter, then comes the cable.
Unless you are going out of your way for an active cable, which will cost a bit more than passive cables, the cables will be relatively inexpensive and their data capability easily identified. Any passive 2 meter USB cable will be capable of only USB 2.0 speeds. They may have USB-C ports on each end and allow a Thunderbolt drive to connect to a Thunderbolt host, but the data will move at USB 2.0 speeds. That may be handy if you don't need to move a lot of data and all you have is the cord that you were using to charge your laptop.
Any USB cable with USB-A on one end may be helpful as well to connect a USB-C drive but depending on the cable it will be limited to USB 2.0 to USB 3.1 speeds. USB-A has half the high speed data pins as USB-C and so tops out at 10 Gbps.
Cables of a meter in length, USB "trident" symbols on the connectors, and USB-C connections on both ends should be able to get 5, 10, or 20 Gbps. There may be a number indicating the speed in Gbps but consider that a minimum since the spec changed so quickly and allowed for cables that met the old 5 Gbps standard to meet the newer 20 Gbps standard.
USB-C cables that are about 3/4 meter in length should be capable of the highest speeds USB-C offers. Some of the cheaper cables will have no markings but should still work but cables certified for 40 Gbps will have the Thunderbolt icon with a number 3 or 4, and or a USB trident icon and a 20 or 40.
I know this is long but the point is to lay out the different bits and how they can affect the performance. If we assume a MacBook Pro with Thunderbolt 3 or USB4 then you have a host capable of supporting drives from USB 1.1 to TB4/USB4, 1.5 Mbps to 40 Gbps. On the other end is the drive, and knowing what that drive can do is a matter of looking at specs, and maybe reading some reviews. In the middle will be the drive enclosure and the cable. Chose those to match your host and drive.
That may be more than you need to know but I hope it helps.