The COVID-19 pandemic has sparked an urgent need to uncover the underlying biology of this devastating disease. Though RNA viruses mutate more rapidly than DNA viruses, there are a relatively small number of single nucleotide polymorphisms (SNPs) that differentiate the main SARS-CoV-2 clades that have spread throughout the world. In this study, we investigated over 7,000 SARS-CoV-2 datasets to unveil both intrahost and interhost diversity. Our intrahost and interhost diversity analyses yielded three major observations. First, the mutational profile of SARS-CoV-2 highlights iSNV and SNP similarity, albeit with high variability in C>T changes. Second, iSNV and SNP patterns in SARS-CoV-2 are more similar to MERS-CoV than SARS-CoV-1. Third, a significant fraction of small indels fuel the genetic diversity of SARS-CoV-2. Altogether, our findings provide insight into SARS-CoV-2 genomic diversity, inform the design of detection tests, and highlight the potential of iSNVs for tracking the transmission of SARS-CoV-2.