Hi.

If I plug "USB 3.0 Header" (Pic1) into motherboard 3.1 Socket (Pic2) am I gonna get 3.1 ? Inside box there is only "USB 3.0 Header" but no "USB 3.1 Header". So I wonder why this mobo has the output if no external output like Gigabyte GC-USB 3.1 BAY
 
Pic1

 
Pic2

 

You should get what ever speed the Device is that you plug into the Port.
If you Plug in a 2.0 Device then you will get 2.0 Speed
If you Plug in a 3.0 Device then you will get 3.0 Speed
On The Header you have circled in Red
 
The Other Header is the 3.1 Header to the Right of the one you have  circled in Red that is. 
If you Plug in a 2.0 Device then you will get 2.0 Speed
If you Plug in a 3.0 Device then you will get 3.0 Speed
If you Plug in a 3.1 Device then you will get 3.1 Speed
See Page 11 http://www.evga.com/support/manuals/files/151-SS-E179.pdf
The USB 3.0 & 3.1 Headers are the same Headers. Type C Connectors are new to USB 3.1
 
You would have wonder over on Gigabyte's website to see why the Gigabyte GC-USB 3.1 BAY sGC-USB 3.1 BAY Motherboards do what they do.
One is an EVGA MB the other is a Gigabyte MB this in my book would be Why.