Humans have approximately 30,000 genes. These genes are sequences that appear in our DNA which is divided up amongst our 23 chromosomes. Offspring receive these genes from their two parents so during meiosis we receive some genetic material from our mother and some from our father. There is about a 50% chance of receiving the mother's gene and a 50% chance of receiving the father's gene for each of the 30,000 genes involves. (The details are more complicated, see [1].)
So yes, statistically one could with probability of something like 1/(2^30000) receive a complete different set of genes than a sibling. In the real world, one will always share around 50% of ones genes with a sibling.
[1] https://www.genome.gov/genetics-glossary/Crossing-Over