As noted by many when the use of ontologies began to extend and the number of ontologies expanded, a need arose to integrate ontologies also arose. An obvious approach is to aggregate or merge them, just adding parts to obtain a single ontology. Such a merger which would have all the vocabulary (object, relations attributes of the individual parts. But there are obvious differences in vocabulary and conceptualization between different ontologies so the task in not so simple and various types of "harmonization" were distinguished. (2JP9)
Usually Ontology Alignment is the term for the weakest form of integration. it requires minimal change, but it can only support limited kinds of interoperability. It is useful for classification and information retrieval, but it does not support deep inferences and computations. (2JPA)
More advanced is Ontology Partial Compatibility: Requires more changes in order to support more extensive interoperability, even though there may be some concepts or relations in one system or the other that could create obstacles to full interoperability. (2JPB)
The topic of sharing, harmonizing and and merging ontologies is discussed by John Sowa at: (2JP1)
http://www.jfsowa.com/ontology/ontoshar.htm#s6 (2JP2)
Sowa distinguishes various concepts such as alignment, merging, unification and integration. In his view an alignment centers on the terms from different ontologies and is "essentially the same as the problems of aligning words from the vocabularies of different natural languages." (2JP3)
alignment. A mapping of concepts and relations between two ontologies A and B that preserves the partial ordering by subtypes in both A and B. If an alignment maps a concept or relation x in ontology A to a concept or relation y in ontology B, then x and y are said to be equivalent. The mapping may be partial: there could be many concepts in A or B that have no equivalents in the other ontology. Before two ontologies A and B can be aligned, it may be necessary to introduce new subtypes or supertypes of concepts or relations in either A or B in order to provide suitable targets for alignment. No other changes to the axioms, definitions, proofs, or computations in either A or B are made during the process of alignment. Alignment does not depend on the choice of names in either ontology. For example, an alignment of a Japanese ontology to an English ontology might map the Japanese concept Go to the English concept Five. Meanwhile, the English concept for the verb go would not have any association with the Japanese concept Go. (2JP4)
integration. The process of finding commonalities between two different ontologies A and B and deriving a new ontology C that facilitates interoperability between computer systems that are based on the A and B ontologies. The new ontology C may replace A or B, or it may be used only as an intermediary between a system based on A and a system based on B. Depending on the amount of change necessary to derive C from A and B, different levels of integration can be distinguished: alignment, partial compatibility, and unification. Alignment is the weakest form of integration: it requires minimal change, but it can only support limited kinds of interoperability. It is useful for classification and information retrieval, but it does not support deep inferences and computations. Partial compatibility requires more changes in order to support more extensive interoperability, even though there may be some concepts or relations in one system or the other that could create obstacles to full interoperability. Unification or total compatibility may require extensive changes or major reorganizations of A and B, but it can result in the most complete interoperability: everything that can be done with one can be done in an exactly equivalent way with the other. (2JP5)