Disclaimer: Not remotely an expert at biology, but I will try to explain.
One can think of the word "gene" as having multiple related uses.
Use 1: "Genotype". Even if we have different color hair, we likely both have the same "gene" for hair which could be considered shared with chimpanzees. If you could re-write DNA nucleobases, you could change your hair color without changing the gene itself, you would merely be changing the "gene encoding". The word "genotype" refers to a "function" which takes in a "gene encoding" and outputs a "gene phenotype"
Use 2: "Gene phenotype". If we both have the same color hair, we would have the same "Gene phenotype". Suppose the genotype for hair is a gene that uses simple dominance. In this case, we could have the same phenotype even with different gene encodings. Suppose you have the gene encoding "BB" whereas I have the gene encoding "Bb". In this case, we could both have black hair, the same "Gene phenotype", but have different "Gene encodings".
Use 3: "Gene encoding". If we have different color hair, then we have different gene encodings (but we have the same "genotype" as described in "Use 1"). This "gene encoding" is commonly not shared between siblings and less commonly shared between species.
So "we share 99% of our genes with a chimpanzee" likely refers to "Genotype".
"95% of our genes with a random human" likely refers to "Gene phenotype".
"50% of our genes with a sibling" likely refers to "Gene encoding".
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