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Much like the definition on this site, the definition of a "Christian" artist tends to be "any group that claims itself as such."
Much of the rise of Western Music can be attributed to the harmonization of the mass and other sacred music - Bach would sign his work "S.D.G," sola Dei gloria - for God's glory alone - but he is rarely considered a "Christian musician." Robert Greenburg in How to Listen to and Understand Great Music delves much more deeply into the historical connection of the church and western music.
In contemporary times, "Christian Contemporary Music," including the likes of Michael W. Smith, Petra, Degarmo & Key, Amy Grant, Steven Curtis Chapman, and similar people, is itself a branding term that tends to encompass a certain style of music that often gets picked up by "praise and worship bands" at contemporary churches. Indeed Jon Acuff (Stuff Christians Like) mentions that these P&W bands often release their own CDs, and clearly fall in this category. Many of the luminaries of the band (e.g. Michael W. Smith) serve as Worship Ministers in their own churches.
Amy Grant, however, helped to define the term when she transitioned from being a "Christian" musician to a more mainstream one. (Russ Taff did the same move but didn't get nearly the same amount of press.) When she released "Baby, Baby," she did so explicitly under the guise that she wanted to do more mainstream stuff. In reaction, many Christians still wanted to claim she was a "Christian artist," despite Grant's desire to "move on."
From the NY Times, 5/11/02:
A writer in the evangelical magazine Christianity Today criticized Ms. Grant's 1997 release, ''Behind the Eyes,'' for its ''complete absence of explicitly Christian lyrical content.'' The ensuing controversy prompted the Gospel Music Association to adopt content requirements for its annual Dove Award entries.
In 2009, Bob Carlisle's secular "Butterfly Kisses" won the coveted "Song of the Year" from the Gospel Music Association's "Dove Awards" - the premier CCM award. According to industry insiders, the GMA was embarrassed that a song without any "Christian" content was voted the coveted "song-of-the-year". To that end ...
Gospel Music Association (GMA) Awards and Criteria Committee has created criteria for eligibility of Dove Awards based on lyric contents. The definition states:
"Gospel music is music in any style whose lyric is: substantially based upon historically orthodox Christian truth contained in or derived from the Holy Bible; and/or an expression of worship of God or praise for His works; and/or testimony of relationship with God through Christ; and/or obviously prompted and informed by a Christian world view."
The only previous requirement for Dove Awards was simply — Christian retail store distribution. In other words, if it was sold in so-called Christian stores it was eligible.
(Reference, but be warned, it gets weird...)
In the end, "Christian" is as much a brand as an actual adjective. The wide spectrum of CCM has no branding authority, so it kind of is was it is.