Shortening journal titles is a useful practice, especially when using mobile devices. Mousing over a journal title in PubMed it will display the full journal title.
The National Library of Medicine provides the guidelines we use to abbreviate journal titles. Since 2007, these have also been based on rules established by the ISSN Center. You may encounter different journal abbreviations for older tittles.
This Fact Sheet gives an outline of the abbreviation guidelines and examples.
You can search journals in the National Library of Medicine (NLM) catalog and get the journal abbreviations.