Master schema represents a predefined or runtime-generated schema accessible via UI. During schema merging master schema always represents a "target" schema.
Factory Default Master Schema
A master schema supplied with the installation. It gets installed to installation folder and copied to the user data cache folder on the first run. In case there's factory default master schema then no schema merging takes place, and master schema is used as is.
Partial schema is a single schema representing a building block of master schema. Partial schema cannot be the master schema, and vice-versa.
A partial schema specific to certain domain of use, i.e. Survey schema is specific to geodesy. It also represents sort of graphical and alphanumerical "standard" (data model) related to targeted domain. Unlike extension-specific schema, content of domain-specific schema is not known beforehand. It could be changed by authorized users via Schema Factory application, to suite users' specific needs. Since multiple schemas may get merged on the target computer, it's possible to offer multiple domain-specific schemas during installation and let the user picks domains of use he's authorized to work against.
A partial schema specific to certain extension. For example, COGO.schema.xml is specific to Survey. Extension-specific schema is known beforehand, and is strongly related to actual extension's hard-coded object model. Users should not be able to change its contents beyond stylization.
A partial schema sitting on remote URL - either inside LAN or across domain boundaries. It's quite common that large organizations provide strict standards across its departments or subcontractors, prohibiting using other standards than prescribed ones. By mandating a schema organization ensures identical outputs for both data and geometry, also prohibiting users change schema stylization. In reality this happens very often, i.e. AGIV provides common graphical and alphanumerical data model, and could possibly host their own schema accessible via HTTP.
Remote schema is partial because users may have locally installed extensions carrying extension-specific schemas as well. Therefor local extensions "prevent" remote schema to play a master schema role.