Bear, relate, pertain, appertain, belong, apply are comparable when used intransitively with the meaning to have a connection, especially a logical connection.
One thing bears on or upon another thing when the first touches so directly upon the second (usually something in question) as to carry appreciable weight in its solution or in the understanding of issues it involves.
One thing relates to another thing when there is some connection between them which permits or, more often, requires them to be considered together with reference to their effect upon each other.
The connection implied is usually closer in the intransitive than in the transitive verb (see JOIN), being commonly one of dependence or interdependence.
One thing pertains or appertains to another when there is a connection that permits their association in practice or thought.
Both of these words are more widely applicable than bear and relate, for they cover not only the connections specifically implied in those words but also those close connections implied by belong and those remote connections implied by have to do with; thus, the things that pertain to happiness are all the things that can be thought of as causing, contributing to, preventing, or affecting the quality of happiness.
Pertain more often implies a necessary connection or a very close relation than the more formal appertain, which commonly suggests an incidental or acquired connection.
Belong, usually with to, implies a relation in which one thing is a part or element without which another cannot exist, function, have its true character or being, or be complete.
In this sense a thing that belongs is a property, an attribute, a duty, or a proper concern.
But belong also may be used of things as they pertain to persons, then implying possession or informally of persons with reference to their qualifications for fitting into a group, especially a social group.
Apply, also with to, implies a relation in which a more inclusive category (as a law, a principle, a rule, a theory, a general term) covers a less inclusive specific instance, usually also explaining, interpreting, or describing the latter or having some clear bearing upon it.