From Science Europe Data Glossary
Definition: public data is information that can be freely used, reused and redistributed by anyone with no existing local, national or international legal restrictions on access or usage.
Alternative definition: public data is non-personal, unclassified and non-confidential data collected or created by an agency in carrying out its functions or statutory responsibilities, and funded from government budgets.
Explanation: public data is a near-synonym of open data, especially according to the first definition. However, in the alternative definition public data may still have access restrictions that open data does not have, such as the requirement of registration before use or permission request for use. In practice, a lot of publicly funded data is not accessible at all.
References: http://searchcio.techtarget.com/definition/public-data; http://blogs.worldbank.org/dmblog/open-vs-public-data-the-big-difference; http://www.opendatanow.com/2013/11/new-big-data-vs-open-data-mapping-it-out/; http://blog.spotcrime.com/2014/04/open-data-vs-public-data-vs-proprietary.html