VMC
Verified Mark Certificate is intended for registered trademarks or qualified government marks. In Gmail, VMC can enable a logo and a blue verification checkmark.
CMC
Common Mark Certificate helps brands use BIMI without a classical registered trademark, but it does not provide the Gmail blue checkmark reserved for VMC.
Technical conditions
BIMI requires SPF/DKIM, enforcing DMARC, a BIMI DNS record, a compliant SVG logo and HTTPS hosting of required files.
Mailbox providers differ
Gmail requires VMC or CMC for BIMI display and gives the checkmark only with VMC. Other providers can apply their own reputation rules.