Should the distinction between bibliography and reference be maintained when writing a paper? There is a small difference between a bibliography and a reference: the former includes all works consulted and the latter only those that are cited in the paper. Should we maintain this technical distinction when writing a paper?

Some journal templates require the title of the last section to be 'References'. Does this mean all the references must necessarily be cited in the paper?
From a practical point of view, whenever you send your paper for a peer review, they check if you have all citations both in your text and in sources. It means that "yes" they must be cited. 

Saying so, there is normally clear advise from a journal how to cite and produce bibliography. You should do what it says.

At last you can always solve the problem by adding one sentence in your text: "Additional information about ... can be found in [your references]." With this sentence everyone should be happy.