The first thing you need to understand is the type hierarchy. In acs 4.x, the type hierarchy is as follows:
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<pre>
acs_object_type
party
group
person
user
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In the acs 4.x groups system, the relation to a group is represented by the party object regardless of whether the relation is between a group and a person or a group and another group. The implication of this is that a person or another group can be a member in a group.
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As far as relationships, composition or membership relations determine whether memberships are transitive. If you have a membership relation with group A and group A has a composition relation with group B, then you are also considered to be a member of B. Group A is like a sub-grouping of group B in this case.
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On the other hand, if you have a memberhip relation with group A, and group A has a membership relation with group B, you are not then considered a member of B. composition relations are transitive while membership relations are not.