Not any software application that is accompanied by its source is open source, albeit many people who are new to the term would be tempted to think that. It is possible to write non-open-source software while accompanying it with the source.
Examples for such cases are:
The Microsoft Visual C++ Run-Time Library and the Microsoft Foundation Classes (MFC), that are accompanied with their source.
xv - a popular shareware image viewer and manipulator for X-Windows that has been distributed with its source code. Note: it is no longer actively maintained, and its developer can no longer be actively reached, and so its use is no longer recommended.
qmail - a popular mail server whose source code was available and can be deployed free of charge, but its licensing terms specified that it is illegal to distribute modified binaries or sources (at least outside the organization) This is enough to make it non-open-source, but it still had been a very popular program. More recently, the source of qmail, and several related programs by the same author, were made public domain, which now makes it open-source software.
None of these packages qualify as free software, but they are all accompanied with the source. There are many others around. A quick search on the Freecode directory of UNIX software will find many such packages.
In order for a program to be open-source it needs to be free of various restrictions as specified in the open-source definition. To be free software as well, it must be also free of some other restrictions. [5]
I believe the term open-source is a bit dangerous in this regard. Then again, free software may not automatically be associated with freedom and liberty, so it isn’t perfect either. But I guess finding a description that accurately describes it in a short space is not very possible, so these terms will have to do.
[5] In a query given by an Israeli Member of the parliament in the past, to an Israeli Defence Force (IDF) representative about whether all the software used by the Israeli military is open-source, the latter interpreted open-source software as software that the IDF has access to its source. This is an even more radical deviation from the correct meaning.