USB 3.0, USB 3.1 gen 1, and USB 3.2 gen 1x1 are all names for the same thing, the 5Gbps speed.
USB 3.1 gen 2 and USB 3.2 gen 2x1 are both names for the same thing, the 10Gbps speed.
USB 3.2 gen 2x2 is the 20Gbps speed.
The 3.0 / 3.1 / 3.2 are the version number of the USB specification. The 3.0 version only defined the 5Gbps speed. The 3.1 version added a 10Gbps speed, called it gen 2, and renamed the previous 5Gbps speed to gen 1. The 3.2 version added a new 20Gbps speed, called it gen 2x2, and renamed the previous 5Gbps speed to gen 1x1 and the previous 10Gbps speed to gen 2x1.
There's also a 3.2 gen 1x2 10Gbps speed but I've never seen it used. The 3.2 gen 1x1 is so ubiqitous that it's also referred to as just "3.2 gen 1".
And none of this is to be confused with type A vs type C ports. 3.2 gen 1x1 and 3.2 gen 2x1 can be carried by type A ports, but not 3.2 gen 2x2. 3.2 gen 1x1 and 3.2 gen 2x1 and 3.2 gen 2x2 can all be carried by type C ports.
Lastly, because 3.0 and 3.1 spec versions only introduced one new speed each and because 3.2 gen 2x2 is type C-only, it's possible that a port labeled "3.1" is 3.2 gen 1x1, a type A port labeled "3.2" is 3.2 gen2x1, and a type C port labeled "3.2" is 3.2 gen 2x2. But you will have to check the manual / actual negotiation at runtime to be sure.
USB 3.0, USB 3.1 gen 1, and USB 3.2 gen 1x1 are all names for the same thing, the 5Gbps speed.
USB 3.1 gen 2 and USB 3.2 gen 2x1 are both names for the same thing, the 10Gbps speed.
USB 3.2 gen 2x2 is the 20Gbps speed.
The 3.0 / 3.1 / 3.2 are the version number of the USB specification. The 3.0 version only defined the 5Gbps speed. The 3.1 version added a 10Gbps speed, called it gen 2, and renamed the previous 5Gbps speed to gen 1. The 3.2 version added a new 20Gbps speed, called it gen 2x2, and renamed the previous 5Gbps speed to gen 1x1 and the previous 10Gbps speed to gen 2x1.
There's also a 3.2 gen 1x2 10Gbps speed but I've never seen it used. The 3.2 gen 1x1 is so ubiqitous that it's also referred to as just "3.2 gen 1".
And none of this is to be confused with type A vs type C ports. 3.2 gen 1x1 and 3.2 gen 2x1 can be carried by type A ports, but not 3.2 gen 2x2. 3.2 gen 1x1 and 3.2 gen 2x1 and 3.2 gen 2x2 can all be carried by type C ports.
Lastly, because 3.0 and 3.1 spec versions only introduced one new speed each and because 3.2 gen 2x2 is type C-only, it's possible that a port labeled "3.1" is 3.2 gen 1x1, a type A port labeled "3.2" is 3.2 gen2x1, and a type C port labeled "3.2" is 3.2 gen 2x2. But you will have to check the manual / actual negotiation at runtime to be sure.