A demurrer is ‘a pleading used to test the legal sufficiency of other pleadings’. A ‘pleading’ is the term used to refer to documents that are presented before court. Documents such as complaints, answers to complaints and cross-complaints are all considered pleadings.
A motion for summary judgment is filed by a party to a case when they believe that there is no dispute as to any material facts and therefore no requirement of hearing evidence and going through the process of trial to determine disputed facts. Alternatively, it could also be explained as follows: if the facts are such that even if they are considered in the manner most favorable to the non-moving party (i.e., not the party who has moved the court for summary judgment) a reasonable jury would not possibly find in favor of the non-moving party. In layman’s terms, this means that the facts of the case are so one-sided that it can be decided in favor of one party without even going to trial.