First a few points.
You are configuring on router R1.
Static routes consist of 1) the prefix that is the destination where you want to send traffic, 2) which way to send packets out for that prefix.
If the way out is over a serial interface, all you need to do is specify over which serial interface you need to send traffic out. Serial interface means there is only 1 router on the other side of the interface. So you can't miss it.
On the other hand, over an ethernet interface, there could be multiple other routers. So you need to specify which of those routers you want to send traffic to. (To reach that destination for which you configure the static route). Therefor the static-route-command allows you to configure the next-hop IP-address. In stead of the outgoing interface.
If you tell the router the next-hop IP-address of a static route, that is usually enough for the router to understand over which interface to send the traffic out. In the routing-table, it has entries for all directly connected networks. And there it can find the next-hop ip-address. Easy.
But here we deal with IPv6. And link-local addresses. If you configure a link-local address as next-hop, that is not enough for the router to figure out which interface to send the packet out over. Because on every link (= every interface), there might be a router on the other side using the exact same link-local address. Because link-local addresses are not unique in the world. Or unique in your network. They are only unique on one single link. One single LAN, or one single p2p serial interface. Therefor in this case, you need to configure more. You need to also configure the outgoing interface.
You configure something on R1.
Therefor, in the static routes, you can use only interfaces of R1. A router knows about IP-addresses. And MAC-address. (And more types of addresses maybe). But it doesn't know how another router names its interfaces. The other routers might not be ciscos. They might be Nokia routers, or Juniper routers. And even then, you still don't know what name the other router gave to the interface you are conneting to.
But you know the name of the outgoing interface on your own router. That's G0/1 in the first picture. So that is the name of the outgoing interface that you use in your configuration command.
If you understand this, maybe you will understand the pictures in your second post too.