It seems some sites arbitrarily restrict "gene map" to only a single chromosome, but others don't. Supposing we don't restrict it to just a single chromosome, is it different from "genome"? Are these two terms just synonyms?
This question can be easily answered by reference to reputable sources on the internet, but as it is important to encourage the general use of the term, Genome, I shall cite examples.
WHAT IS A GENOME?
A genome is an organism’s complete set of DNA, including all of its genes
the arrangement of genes on a chromosome
This is actually definition 3 of map in the dictionary — i.e. a variant on topological maps. The scientific usage is made clearer in the following:
DNA mapping refers to the variety of different methods that can be used to describe the positions of genes. DNA maps can show different levels of detail, similar to topological maps of a country or city, to indicate how far two genes are located from one another.
Distinction in a nutshell
A Genome is an entity — a Genetic Map is a graphical representation of features of that entity.
Hence the following sentence makes sense:
There is no genetic map for the genome of Bacillus obscurus.
The two terms are certainly not identical. The confusion of the poster may relate to the practical limitations of representation such that often the map of only one chromosome is presented at a time.
Gene map is the spatial arrangement of genetic markers and the relative distance between each of them. While the genome includes the entire hereditary information of the organism; this includes both genes and the non-coding sequences of DNA (introns).