The plugs differ for solid or stranded use.
Not what i listed the ones i listed are suitable for both cable types. You will be hard pressed to find stranded only CAT6/6A connectors nowadays (CAT 5 you can still easily get both)
The images here explain what are for which cable...
http://www.l-com.com/content/Article.aspx?Type=N&ID=10460
90% of CAT6 connectors nowadays are the types which straddle rather than pierce. I have personally used what i linked to on both cable types as i stated.
solid cat6 has a different awg than stranded, so won't fit.
No it does not CAT5E and CAT6 cable is either 26AWG 24AWG or 23AWG be it stranded or solid core. VERY FEW CAT5E cables are still 26AWG and VERY FEW CAT6 cables are 23AWG (though technically that is the spec for CAT6) still makes no difference to the connector crimp as a guide A 23AWG cable is 0.57mm wide, while a 24AWG cable is 0.52mm wide
CAT 6 cable is thicker physically and visually due to a thicker sheath (cover) and the plastic internal cross spine which separates the pairs.
The internal wire gauge is the same that being either 26AWG 24AWG or 23AWG (decent CAT5E and more than good enough CAT6 cable will be 24AWG).
CAT6 connectors have a larger opening to accept the thicker sheath and spine in the cable.
The issue is that a plug for stranded is designed to piece through the strands to form a contact, it can't do this with solid core cable, hence the plugs are different. The contacts for solid are split so they go around the solid core on both sides to conform.
Yep with CAT6 cable though "most" of the time if you buy half decent (2 part or greater) connectors they will work on both, here is also an overseas retailer selling the same connectors i pointed to and specifically saying the are suitable for both....
http://www.showmecables.com/product/Cat6-Connector-With-Guide.aspx