The short answer to this is 90% of the time nothing. Most laser cutters and most laser engravers are identical. You will find however that there is a class the only laser engrave or laser cut but these tend to be high-end industrial machines for metal applications. Sometimes you'll see some smaller diode lasers that are just designed to engrave as well.
With CO2 machines the real trick here is how powerful is it. A 60 W machine tends to be the perfect balance between engraving encoding for most people but be warned if you start going up in power it's going to start reducing the Quality of your engraving. An 80 W laser engraver also does a great job at both of them but once you start going to 100w and above you're really going to notice a quality difference.