What is a difference between cross-lingual IR and multi-lingual IR?
In this paper they differentiate between these two terms as follows:


  While CLIR is concerned with retrieval for given language pairs (i.e.
  all the documents are given in a specific language and need to be
  retrieved to queries in another language), MLIR is concerned with
  retrieval from a document collection where documents in multiple
  languages co-exist and need to be retrieved to a query in any
  language. MLIR is thus inherently more difficult than CLIR.