A layer 3 switch does not just “glean” information from the packet , it can switch packets and rewrite IP header data at wire speed to place packets on different networks completely bypassing a router.
I don’t know of any better term for it than a “layer 3 switch”.
But these are not “straightforward” concepts - you say there is no “hybrid” thing - but there most certainly is: https://en.wikipedia.org/wiki/Bridge_router