Logos = Word (general biblical truth)
Rhema = Word (specific application)
The Greek synonyms, "Logos" and "Rhema," are translated in the English Bible as "word". However, Dr. Bill Hamon argues that Logos refers to the scriptures as a whole or to Jesus, whereas Rhema refers to the individual scripture which applies to us individually.
Hamon likens Logos to a well of water and Rhema to a bucket of water from that well.
John 1:1
In the beginning was the Word....
and Hebrews 4:12
For the word of God is ...sharper than any twoedged sword.
are prominent examples of Logos found in the New Testament.
While Luke 1:38
And Mary said, ...be it unto me according to thy word.
and Luke 5:5
And Simon answering said ...nevertheless at thy word I will let down the net.
are examples of Rhema.
Here's a video of Jim Logan explaining the difference between Logos and Rhema:
According to Jim Logan, Logos refers to the scripture, word for word, whereas Rhema refers to the application of the scripture in our life.
The Rhema Doctrines of the charismatic Christians however may not be shared by the non-charismatic Christians.
For one group (the charismatic Christians), the term Rhema has a doctrinal significance which the other group (the non-charismatic Christians) may take issue with.