The problem with finding a term to describe what the OP calls ‘a "contains" relation’ is a reflection of the fact that in many situations, English speakers don’t seem to have felt the need to devise abstract categorizations of this sort; or if they have, they are often restricted to particular domains, such as mathematics.
To take one notable example, there doesn’t even seem to be a general abstract term to describe the relationship between siblings, at least in dictionaries: the metadictionary Onelook.com returns no hits for plausible terms like siblingdom, siblingry or siblingship. When the need for a similar term does arise, it is usually spelled out in specifics: brother-sister relationship, sister-sister relationship.
I think one of the reasons for the lack of a general term for a container-contained object relationship is that in everyday situations it is rarely necessary to describe such a relationship in abstract terms. Usually, the context requires a much more explicit description:
“Please replace the cutlery in the drawer after use”
“The cat is in the box again!”
“The hold of the ferry accommodates up to 25 buses or 45 passenger cars”.
The lack of mutuality between the containing object and the object contained presents a further difficulty when one attempts to encapsulate the relationship using a single term. The best I can come up with is inclusion relationship (the same suggestion as that proposed by GMB and hauron).