[b] What is the difference between the "Hague Conference" and the "Hague Conventions"?

The term "Hague Conference on Private International Law" refers to the name of the intergovernmental organisation, whose purpose is "to work for the progressive unification of the rules of private international law" (Article 1 of the Statute of the Hague Conference). The principal method used to achieve this goal consists in the negotiation and drafting of multilateral treaties, which are called "Hague Conventions".
Between 1893 and 1904 the Conference adopted seven international Conventions, all of which have been subsequently replaced by more modern instruments. From 1951 to 2005 the Conference adopted 36 international Conventions. Until 1960 the Conventions were drafted only in French; since then they have been drawn up in French and English. Among the texts which have been the most widely ratified should be mentioned the Conventions on civil procedure, on service of process and on taking of evidence abroad, the Convention Abolishing the Requirement of Legalisation for Foreign Public Documents, the Convention on the Conflicts of Laws Relating to Testamentary Dispositions, the Conventions dealing with maintenance obligations, the Convention on the Recognition of Divorces and Legal Separations and the Conventions on the protection of minors, on the Civil Aspects of International Child Abduction, and on intercountry adoption.
Some of the Hague Conventions deal with the determination of the applicable law, some with the conflict of jurisdictions, some with the recognition and enforcement of foreign judgments and some with administrative and judicial co-operation between authorities, and some combine one or more of these aspects of private international law.

N.B.: Not all Conventions concluded at The Hague are Conventions of the Hague Conference on Private International Law (e.g. the Hague Conventions of 1964 relating to a Uniform Law on the International Sale of Goods (ULIS) and relating to a Uniform Law on the Formation of Contracts for the International Sale of Goods (ULF)).