Generally, what is is the name for the non-vocal parts of a song that are not interludes or preludes and not a guitar solo or instrumental verse/chorus? For example, right after the acapella vocal intro in Kansas' Carry on My Wayward Son.
In pop/rock music, the commonest terms are:
Pop/rock are informal; rules are made to be broken and you can invent your own names for parts if the de facto standards don't fit. Some songs have more than one verse melody, or more than one type of chorus, and it's quite common to see things like "chorus II".
In your example, you might choose to refer to the "vocal intro" followed by the "guitar intro". Indeed I'd write down the structure of the start of *Carry On Wayward Son" as:
Lots of people, particularly in the rock and roll idiom, would call this the riff. It's an easily recognizable component that defines the song.
Lots of rock songs are similarly defined by, and built around, a particular riff, so it makes sense that one would refer to that section of the song as such.