The genome is the sum of all genes in an organism, while the transcriptome shows which of those are transcribed into RNA and in what proportions. That is, which genes are transcribed more and which genes are transcribed less. Then, the proteome tells us, of the transcribed genes, which are translated and the proportion (which transcripts lead to more protein molecules and which to fewer).
Work Step by Step
Essentially, the genome, transcriptome, and proteome correspond with the three steps of information flowing through the cell, from DNA to RNA to protein. Added to this is information about the relative levels of expression since it is changed, from one gene to another, at each step of the flow from DNA to RNA to protein.