For example: What is the difference between the meaning of "Health centers which conduct free medical check-ups..." and "Health centers conducting free medical check-ups..."? Thank you in advance.
 Health centers [which conduct free medical check-ups].
 Health centers [conducting free medical check-ups].
The difference is mainly a syntactic one.
Gerund-participial and past participial clauses as modifiers in NP structure are semantically similar to relative clauses. Leaving aside the progressive aspectuality in , the two constructions have similar meanings, though the subordinate modifying clauses are different.
In  the bracketed constituent belongs to the class of integrated relative clauses while that in  is a non-finite clause -- more specifically a gerund-participial clause.
Both sentences have the same meaning, but they differ structurally. The first one is a complex sentence with a relative clause /starting with 'which'/. The second one is a simple sentence with an attribute /expressed by a participal construction/.