Halliday & Matthiessen (2014: 295):
If the relationship of possession is construed as the Process, then two further possibilities arise.
Either (1) the possessor is the Carrier and the possessed is the Attribute (we will call the thing possessed the ‘possessed’ rather than the ‘possession’, to avoid ambiguity; ‘possession’ refers to the relationship), as in Peter has a piano. Here piano-ownership is an attribute being ascribed to Peter. Verbs other than have combine the sense of possession with other features, e.g. lack ‘need to have’, boast ‘have as a positive feature’.
Or (2) the possessed is the Carrier and the possessor is the Attribute, as in the piano belongs to Peter. Here Peter-ownership is an attribute being ascribed to the piano. Neither of the two, of course, is reversible; we do not say a piano is had by Peter, or Peter is belonged to by the piano.