The coronavirus disease 2019 pandemic, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a major public health concern. A handful of static structures now provide molecular insights into how SARS-CoV-2 and SARS-CoV interact with its host target, which is the angiotensin converting enzyme 2 (ACE2). Molecular recognition, binding and function are dynamic processes. To evaluate this, multiple all atom molecular dynamics simulations of at least 500 ns each were performed to better understand the structural stability and interfacial interactions between the receptor binding domain of the spike protein of SARS-CoV-2 and SARS-CoV bound to ACE2. Several contacts were observed to form, break and reform in the interface during the simulations. Our results indicate that SARS-CoV and SARS-CoV-2 utilizes unique strategies to achieve stable binding to ACE2. Several differences were observed between the residues of SARS-CoV-2 and SARS-CoV that consistently interacted with ACE2. Notably, a stable salt bridge between Lys417 of SARS-CoV-2 spike protein and Asp30 of ACE2 as well as three stable hydrogen bonds between Tyr449, Gln493, and Gln498 of SARS-CoV-2 and Asp38, Glu35, and Lys353 of ACE2 were observed, which were absent in the SARS-CoV-ACE2 interface. Some previously reported residues, which were suggested to enhance the binding affinity of SARS-CoV-2, were not observed to form stable interactions in these simulations. Stable binding to the host receptor is crucial for virus entry. Therefore, special consideration should be given to these stable interactions while designing potential drugs and treatment modalities to target or disrupt this interface.