Al Idraj is a saying not of the Prophet's (May God's blessings and peace be upon Him), and is sometimes on the part of the narrator, either to clarify a word or to make a saying of the Prophet (May God's blessings and peace be upon Him) more complete. A Wad' means fabrication. So, what is the difference between Al Idraj wal Wad' (الإدراج و الوضع)?
The difference is simple:
In case of Al Idraj, the narrator does not claim that the part the explains or clarifies the hadith from the prophet words -peace be upon him-. In many hadiths the distinguish is made explicit, for example after narrating the hadith the person says and
I say and then explain or clarify the meaning.
However, in the fabricated hadith the narrator completely make the entire hadith from his/her mind and claim it to be from the prophet sayings -peace be upon him- .