Gene expression and protein expression are absolutely not the same thing. While counts of mRNA levels for a particular gene may give some indication of how much protein is present, many times it does not. Similarly, quantitating protein levels does not necessarily mean the relative levels of mRNA will be similar. There are many points for regulation between RNA polymerase rolling along the gene and creating the pre-mRNA and the protein coming out of the ribosome and being folded and transported to its correct place in the cell. mRNA can be silenced, degraded, or prevented from being translated by a number of mechanisms. Proteins themselves are subject to extensive regulation, with half-lives that can vary from seconds to weeks. Of course, genes are regulated in many different ways as well, from repressor proteins to methylated DNA to chemically-modified histones, and the number of polymerase complexes on the DNA and their relative transcription speed are also under regulatory control.
If I replace the DNA sequence of a gene of interest with the GFP DNA; and then subsequently quantify the fluorescence levels, am I measuring the gene expression of the gene of interest OR the protein expression?
You are quantifying the protein levels of GFP. mRNAs can be subject to sequence-specific regulation (such as siRNA), so you can't just say absolutely that GFP levels are equal to your gene product of interest. Many times they will be proportional, but some times they won't, so you'll need to do a number of other experiments to verify your results.