This deals with the connection. The fixed will have a full size plate while the carbine will be a circle. If you're placing this on an AR, you will need the fixed to fixed or fixed to carbine in order to hold the takedown pin spring and detent as this does not accommodate the endplate.
"Fixed" & " Carbine" refers to, A) the type of Stock u want to make foldable &, B) whether ur lower receiver needs retention for a rear takedown pin spring & detent.
If ur using a Fixed Stock (ie: AR15 A2 stock; or stock not requiring a buffer tube) then u will need either the "Fixed to Fixed", which provides the spring & detent retention needed for a rear takedown pin, while also providing the propper mounting surface for a Fixed Stock, or "Carbine to Fixed" if, A) u prefer to use a custom style receiver end plate (ie: ambi sling loop; QD sling mount; etc.) to retain the spring & detent, or B) u have a lower or bolt action rifle chassis that only has a receptacle for a Carbine buffer tube but u prefer to use a Fixed Stock which doesn't utilize one.
If ur planing on using a Carbine Style Stock (Collapsible; M4; etc.) which a receiver extension/buffer tube is proprietary, than u will need either "Fixed to Carbine" or "Carbine to Carbine", again, depending on whether u want/need to use a receiver end plate or not.