Copy number variants - having more or less than the expected two copies of a region of DNA. Can be divided into amplifications and deletions.
Structural variants - rearrangements in the order of sections of the DNA. Can be divided into insertions, deletions, inversions, and translocations (either inter or intra-chromosomal). Can also be complex, involving multiple events at the same location.
Challenges and standards in integrating surveys of structural variation (Nature genetics, 2007).
Please see Figure 1: Lexicon of genomic variation. I was surprised how many types of variants there are.
Really like this paper.
The MISO Sequence Ontology database is a project to provide official definitions for terms related to sequence annotations.
So, if you look in MISO, you will see that they classify Copy Number Variations as a subclass of Structural Variants (link to definition of Structural Variant in MISO)
Please note that in some literature these terms may have been used with different meaning. The official definition is the one in MISO, but everybody has his own version of the definition.