= 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.
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