Then you have obviously never heard of the homeobox genes and the absolutely vast literature on body patterning in vertebrates. You have never explored the deep homology in fins and limbs, and the role of the
same genes (specifically Hoxa11, Hoxa13 and Hoxd10, Hoxd11, Hoxd12 and Hoxd13) in patterning the fins of lobe finned fish and all tetrapods. Here are a few references and links to get you going:
Yano and Tamura, "The making of the differences between fins and limbs", Journal of Anatomy,
here. Excellent review article, with a huge number of references.
Shubin, Tabin and Carroll, "Deep homology and the origins of evolutionary novelty",
Nature 457, 818–823 (12 February 2009), another excellent review article from some of the foremost evolutionary biologists in one of the world's premier journals, covering more than fins and limbs
Davis, Dahn and Shubin, "An autopodial-like pattern of Hox expression in the fins of a basal actinopterygian fish",
Nature 447, pages 473–476 (24 May 2007). A short quote from the abstract: "Here, we report on the expression and function of genes implicated in the origin of the autopod in a basal actinopterygian,
Polyodon spathula.
Polyodon exhibits a late-phase, inverted collinear expression of 5′ HoxD genes, a pattern of expression long considered a developmental hallmark of the autopod and shown in tetrapods to be controlled by a ‘digit enhancer’ region. These data show that aspects of the development of the autopod are primitive to tetrapods and that the origin of digits entailed the redeployment of ancient patterns of gene activity." (The autopod is the hand or foot of tetrapods).
There is a year or more worth of reading if you start with the review articles and work forward and backward (like a new PhD student would do in their first year literature review to get them up to speed in their subject).
Rather than there being genes for fins and genes for limbs which are different, as you would have it, the reality is that the same genes pattern both the fins of fish and the limbs of tetrapods in a deep homology. Surely if you were that knowledgeable about genetics you would know this?