Understanding genetic similarity in humans
Yes, these are different measures, and agreeably confusing. The "more than 99%" figure refers to pairwise distance. This figure (actually 99.9%) means that if you were to line up the 3 billion nucleotides of DNA from of any two people, on average, 1 in 1000 of these nucleotides would be different. Among siblings, this number would be even smaller. The 50% figure refers to the origin of DNA stands in a diploid organism: you get one exact copy of each of your genes from your mother, and an exact copy from your father. So half your DNA comes from each parent. But the DNA from each parent is still nearly identical. Siblings will get all their DNA from their parents, but for any particular section, they will get either their maternal grandmother's or grandfathers gene from their mother, and either their paternal grandfather's or grandmother's gene from their father. 
For reference, you often hear that humans and chimps share 98% of our DNA. This is the not exactly a pairwise difference value, because it only counts changes in amino acids (http://humanorigins.si.edu/evidence/genetics). The amino acids between chimps and humans are about 98.8% identical to humans. The DNA across the whole genome is about 94% identical. There are about 50 genes present in humans that are absent in chimps https://www.genome.gov/15515096/2005-release-new-genome-comparison-finds-chimps-humans-very-similar-at-dna-level