Since not all genes expressed are translated into proteins and protein activity might rely on post-translational modifications (that are not triggered by the genome), both collections of molecules provide a different insight into the (cellular) state of an organism.
The genome is the sum total of genetic information encoded in the organism which is also called genotype of that organism, while the proteome is the outcome of the interaction between environment and the genome which is called phenotype. The proteome of a cell may differ depending on environmental condition or age, while the genome remains unchanged under these conditions (not considering extreme condition causing mutation).
< ... which is also called genotype of that organism...>
An organism's genotype is its specific combination of alleles for a given gene. It does not represent the whole genome. So, for example, in the pea plants, the possible genotypes for the flower-color gene were red-red, red-white, and white-white.
< ...while the genome remains unchanged under these conditions... >
Genome can be changed under stress conditions. Ex, some genes will be methylated...etc (1). Transposons jump around inside the genome can also cause genome change. Some DNA fragments can also be lost under some environmental conditions.
(1) https://www.pnas.org/content/109/32/E2183
Widespread dynamic DNA methylation in response to biotic stress