Distinction

CUI cloud is its own category.

A Cloud Service Provider that processes, stores, or transmits CUI is expected to arrive with authorization and a Customer Responsibility Matrix. That is not the same proof as a managed IT provider assessed against CMMC for services it operates.

Managed IT in the boundaryCSP handling CUI
Typical firmManaged operations, SOC, vCISO tooling on the customer estateIaaS, PaaS, SaaS, GovCloud, enclave host
What CMMC wantsProvider status for in-scope services plus a CRMFedRAMP Moderate or equivalent plus a CRM
Where they listNot this directoryThis directory
Failure modeManaging tools without being in scopeCalling a region CMMC ready without inheritance

If you run managed services on top of your own authorized cloud, apply here for the cloud offering only.