What's the difference between constitutional samples and tumor samples?
Constitutional samples do, as you surmised, refer to germ cells (sperm or ovum). Hence they have 1 copy of DNA instead of 2.

Tumours, as they acquire more mutations, often have aneuploidy, or different numbers of chromosomes, and can also have increased incidence of Xn chromosomes where X > 2. This is polyploidy for humans and organisms with normal 2n chromosomes.