Let's start by examining what genes and chromosomes are. A chromosome is a long section of DNA, and a gene is a section of that chromosome that codes for a particular trait. A gene mutation technically changes a small portion of the chromosome. While all gene mutations are technically also chromosome mutations, not all chromosome mutations are necessarily gene mutations.
Gene mutations are small in scale. It could be that a single base pair was swapped out within a gene. This might result in significant protein changes, but it also might not cause any noticeable differences.
Chromosome mutations are much larger in scale. They can change the number or structure of an entire chromosome. Four common types of chromosomal mutations are duplication, deletion, inversion, and translocation. A duplication occurs when a section of the chromosome's DNA gets duplicated, and the entire chromosome then becomes longer than the original. Deletion is essentially the opposite. A section of the DNA code is deleted, and the chromosome loses that information and becomes shorter. An inversion occurs when a section of the chromosome gets flipped around backward. No information is lost or gained, so the chromosome doesn't change in size or length. Rather, the information is in the wrong order. If you inverted the word "bat," it would become "tab;" the result is a completely different word. This kind of mistranslation characterizes an inversion. A translocation occurs when sections of the chromosome exchange places with chunks of DNA from another non-homologous chromosome.
These chromosomal mutations are much more severe than gene mutations because they affect more of a person's genetic code. Consequently, the chromosomal mutations are likely affecting multiple genes. A gene mutation only affects a single gene.