The words fleshly and carnal in the Bible are both translated from the same Greek words, sarkikos and sarkinos. These Greek words basically mean “controlled by the sensual appetites.” What is lost in the translation is that sarkikos is a much stronger word, indicating that the corrupt nature has been given over to, whereas with sarkinos, it seems more a matter of lacking of self-control to some degree. Since sarkinos is the word used in 1 Corinthians 3:1, it is a much less severe accusation than has often been assumed. Etymologically, the word carnal is from a Latin heritage, whereas the word flesh seems to be more distinctly evolved from Old English.
Those two Greek words are variations of the Greek word sarx, which is usually translated flesh, and has quite a few more nuances of meaning than either fleshly or carnal. (There is one other Greek word, kreas, translated as flesh which distinctly means “meat or that which is eaten.”) Interestingly, while fleshly and carnal are found only a few times in the Bible, flesh appears between 170 and 420 times in the common six Bible translations, leaning heavily toward the 300 or so times of occurrence. I also included the New Living Translation at the end, although it seems to be more of a paraphrase. See the lists below (x= how many times, v=in how many verses):
flesh fleshly carnal_______________
King James Bible 420x, 369v 3x, 3v 11x, 10v_
New King James Bible 335x, 330v 6x, 6v 7x, 6v__
New International Version 170x, 157v 0 0 __
English Standard Version 313x, 283v 0 0_____
New American Standard Version 318x, 280v 8x, 7v 0_____
Revised Standard Version 322x, 292v 0 1x_____
New Living Translation 54x, 51v 0 0_____
The meaning of the word flesh is more varied, and less inherently tied to the idea of uncontrolled behavior, so it is important to not be confused by this. According to Vine’s Expository Dictionary of New Testament Words, there are 13 shades of meaning of flesh in New Testament usage. The understanding is pretty clearly derived from context and phrasing if other meaning is not assumed or forced. For instance, in places like John 1:14 and Galatians 2:20, it is referring to the physical body in a matter of fact way, without any moral implications. It is this meaning that leads to it sometimes being used metaphorically of “all humanity.” Another neutral meaning is when it is used to talk about interactions and responsibilities unavoidably linked to having a physical body in daily life.
It is only when the human body and it’s sensations, emotional or physical, are let to rule the conduct that flesh becomes associated with negative meaning. If people are wrongly relying on man-made wisdom, contrary to God’s truth (not common sense or realities truly discovered, but man-made philosophies made to explain and guide), this is attributed to the flesh nature, as opposed to higher truths. In the final analysis, such human wisdom is a convenient way to rationalize corrupt human desire, including power over others and satisfying every feeling of the moment. Or, in other words, behaviors that tend to destroy us or our relationships with others.
Now, I’ll be one of the first people to tell you that many religious rules about “desires” are just man-made rules. Self-righteous is sometimes carnal dressed up to look religious. The words desire, lust, and flesh get used in religious circles in whispered tones or as smack-downs to keep people in fear and bondage to “authority.” However, none of these words mean bad things. Even lust only really means “strong desire.” It is only destructive when it is allowed to settle on the wrong desire, wrong sometimes by a factor of relationship, not by the act itself. The same Greek word that is translated as lust is also translated positively as desire in Phillipians 1:23 and 1 Thessalonians 2:17.
Just like the stomach is not wicked because we are told not to be gluttons; or the eyes are not evil because we are told to be careful what we look at; and money is not bad because we are warned to not be greedy; we are not polluted by the fact that we have physical bodies. The human body (our flesh) or the methods of taking care of it and enjoying various aspects of this physical life (talking, fishing, walking, drawing, to name a few) are part of this earthly journey. We will suffer and hurt others if we are slaves to our bodily desires, but proper self-control makes this gift of physical life a more beautiful thing.