If the client asks for only PreferMinimalContainer, then this says that it doesn't want ldp:contains AND it doesn't care about links to the pages of content... there's no preference given.
If the client asks for both PreferMinimalContainer AND PreferContainedIRIs, then this says that it doesn't want ldp:contains (and similar) AND it wants the pages to link to ones that have IRIs in them, not pages with full descriptions of the annotations.
The orthogonal nature of the preferences should be (further) clarified in Protocol section 4.2.1
... and should be clarified.
In particular:
If the client asks for only PreferMinimalContainer, then this says that it doesn't want ldp:contains AND it doesn't care about links to the pages of content... there's no preference given.
If the client asks for both PreferMinimalContainer AND PreferContainedIRIs, then this says that it doesn't want ldp:contains (and similar) AND it wants the pages to link to ones that have IRIs in them, not pages with full descriptions of the annotations.
The orthogonal nature of the preferences should be (further) clarified in Protocol section 4.2.1
Thanks @mattmcgrattan!