I can't see any similarities in the music.
This Fire Burns is by a band called Killswitch Engage and I don't think it was written for any wrestler and I assume CM Punk had to get special licensing rights to use it just like he is for Living Color's Cult of Personality he used more recently. Cult of Personality is a song that is 25 years old, I remember that from grade school, uggh just gave away my age.
That's a side trivia question though - what do Cult of Personality and This Fire Burns have in common besides both being hard rock/metal?
From what I remember CM Punk was using This Fire Burns before Killswitch Engage officially released their album "As Daylight Dies". I went to wiki Killswitch Engage and found this so Red might be right:
"On May 23, 2006, the song "This Fire Burns" was released on the WWE Wreckless Intent album.[18] The track was intended to be the new theme song for WWE wrestler Randy Orton; however, it was scrapped and later became the theme song for the WWE Judgment Day 2006 pay-per-view. "This Fire Burns" is formerly used as the entrance theme for WWE wrestler CM Punk (along with his stables the Straight Edge Society and The New Nexus) from 2006 until 2011 and was later re-released as "This Fire" on the As Daylight Dies Special Edition.[19]"