Gene vs. Protein Expression Assays
Gene expression is the production of a functional gene product from a gene. So protein expression is a functional read-out of gene expression for gene loci that encode proteins. 

However, gene expression is frequently, and erroneously, used to refer to measures of mRNA levels. The production of mRNA is a prerequisite step for the production of protein from a gene and it provides information about the transcriptional activity of a gene loci. 

Translation of mRNA is a highly regulated process and 
global assays highlight that mRNA transcript levels explain less than half of the variation in protein concentrations.   


  For example, 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 measuring both gene expression and protein expression from the promoter + GFP gene loci. If you are interested in transcription from the promoter then measuring transcript would provide a more direct measure.