Further to Dan's post, I suggest you check the Wikipedia articles on coconut oil, palm oil, and cetyl alcohol, paying particular attention to the composition of palm oil. The R1, R2, and R3 that Dan shows can be a number of different groups, but are mostly either palmitic acid and oleic acid. Palmitic acid is a saturated C16 straight chain carboxylic acid that can be chemically reduced to the alcohol, giving cetyl alcohol.
So yes, most cetyl alcohol comes from palm oil, but it is a more complicated process - the palm oil is saponified as described by Dan, the palmitic acid is separated, and then chemically reduced to form cetyl alcohol.
So soap made from cetyl alcohol will contain only the cetyl alcohol - soap made from saponification of palm oil will contain glycerol and a mixture of fatty acids composed mostly of palmitic acid and oleic acid. The two soaps should be completely different.
Coconut oil contains smaller R groups than palm oil - it is mostly lauric (C12) and myristic (C14) acid. You will not be able to make cetyl alcohol easily from either of these.