Why doesn’t the USB-c cable from my LaCie external storage device fit in my MacBook Pro thunderbolt 3 ports

If the cable from LaCie does not fit, it's not a USB-C connector (or it's been damaged or crushed).

Some of my LaCie drives have a USB Micro B Super Speed port on the drive, and they come with a cable with that plug on one end and a USB A plug on the other. to connect those drives to a newer Mac, I use a USB-C to -A adapter.

What is the exact model of your MacBook Pro, perhaps you have Thunderbolt 2 instead of Thunderbolt 3.

Identify the ports on your Mac - Apple Support

That's strange. USB-C is the same to every manufacturer. Something else is fiscally wrong with your connectors and ports.

Can you show us an image of the situation, please?