What is the difference between USB 3.0 and USB 3.1 generation 1?

The USB Implementer’s Forum has renamed USB 3.0 as USB 3.1 Gen 1. They are exactly the same thing, though technically speaking, USB 3.0 no longer exists (“If you have a drive in USB 3.0, she’s be waiting in USB 3.1”).

The USB Implementor’s Forum would also be happy if you used "SuperSpeed USB” for Gen1 and “SuperSpeed USB 10 Gbps” for Gen2. Seriously, it’s spelled out in a document here: http://www.usb.org/developers/ssusb/USB_3_1_Language_Product_and_Packaging_Guidelines_FINAL.pdf

Now, see where it says “SUPERSPEED+” in that logo. Apparently, it is not okay to say “SUPERSPEED+” in any consumer-facing documentation, only “SuperSpeed USB 10 Gbps”, presumably out of expectation of future generations. Good enough, but then why the SUPERSPEED+ at all? That is a term from the developer documentation, but not for the consumer. Except in the logo, apparently. It’s no surprise that some folks are confused.

Also note that USB 3.1 is only the signalling convention, NOT the connector or the power supply. The connector type (Type-A, Type-B, Type-C), the power levels (Battery Charging, Power Delivery, etc) are separate USB specifications, not part of USB 3.1. So you can actually have a Type-C port that only supports USB 2.0, for example.