Marketing+Architecture
I've seen the two terms used interchangeably.
'Multilayer' implies that the device is inspecting each packet at all seven OSI layers, versus a packet filtering firewall which operates only at the network layer.
BUT, in order for the Stateful Packet Inspection firewall to operate, it needs to inspect packets at all seven OSI layers.
So, It's the same thing.
So, in effect, it's like saying 'Fully Automatic Transmission' versus 'Automatic Transmission'.
At a high-level, Stateful inspection just means checking to see if packets are behaving the way they are supposed to behave.
Do not confuse 'Stateful Multilayer' with 'Deep Packet Inspection', which is an 'Appliction Firewall' that looks at the CONTENTS of packets at the application layer, to catch viruses/exploits, etc.
http://en.wikipedia.org/wiki/Deep_packet_inspection