Well, the "OSI" model where there's a little disassembly and assembly line in your box, where each layer gets taken off by one robot and the payload of that inside package gets handed off to another concern -- all lies.
The chips that do this (if they've got the features, anyhow) do L2, L3, L4, L5, etc all at the same time. So it's not an L2 switch and L3 router -- it's both at the same time, looking at the whole packet at once.
But -- there is no such thing as an ethernet "router" -- it's just a bridge with a forwarding table populated (usually) by listening for MAC addresses and updating forwarding tables. "flood and learn" There are even less ethernetty things out there that use the ethernet signaling but mechanically populate the forwarding tables of switches.
But a "thing that forwards between vlans" usually means "a thing that forwards packets from one L3 subnet to another."
You could probably make some insane custom switch that has routing rules for forwarding mac address packets from one vlan to another based on a bunch of zany rules, but such a cursed object would be hated universally by all who come after you.
The chips that do this (if they've got the features, anyhow) do L2, L3, L4, L5, etc all at the same time. So it's not an L2 switch and L3 router -- it's both at the same time, looking at the whole packet at once.
But -- there is no such thing as an ethernet "router" -- it's just a bridge with a forwarding table populated (usually) by listening for MAC addresses and updating forwarding tables. "flood and learn" There are even less ethernetty things out there that use the ethernet signaling but mechanically populate the forwarding tables of switches.
But a "thing that forwards between vlans" usually means "a thing that forwards packets from one L3 subnet to another."
You could probably make some insane custom switch that has routing rules for forwarding mac address packets from one vlan to another based on a bunch of zany rules, but such a cursed object would be hated universally by all who come after you.