 Solution

A Fischer carbene complex typically has a low-oxidation-state, relatively electron-rich middle/late transition metal with strong pi-acceptor ligands such as CO. The carbene is treated as a neutral two-electron donor; metal-to-carbene back-donation contributes to its bond, but its carbon remains electrophilic. An OR or NR${}_2$ substituent stabilizes that carbon by heteroatom donation. Here the metal is Cr(0), $d^6$, in an 18-electron pentacarbonyl complex.

A Schrock carbene complex usually contains an early metal in a high oxidation state, often $d^0$, with electron-donating ligands rather than a shell of pi-accepting carbonyls. Its alkylidene has substantial dianionic character in ionic counting, and its carbon is correspondingly nucleophilic. Alkyl substituents are common; heteroatom stabilization of an electrophilic carbon is not the defining feature. These are bonding/electronic limiting descriptions rather than a rule based only on the drawn metal-carbon double bond.