Yes, both of those male plugs are 30A 120V. The top one, the one you have on your trailer is a variation called a "Twist Lock" 30A, while the bottom is just a standard 30A. The reason it is called a "Twist Lock" is you litteraly plug it in and give it a little "twist to lock" it in place, where the standard 30A plug could potentially be pulled out. Having the twist lock on the trailer is a means of securly connecting the shore power cord to the trailer. I had never seen one of these either before my inlaws bought their TT which had this same connection, my TT has the permanent cord like your other TT.
Yes, a longer version of the third picture is what you need, but it needs the screw on collar like the yellow cord pictured.
