Single atom catalysis (SAC) is a recent discipline of heterogeneous catalysis for which a single atom on a surface is able to carry out various catalytic reactions. A kind of revolution in heterogeneous catalysis by metals for which it was assumed that specific sites or defects of a nanoparticle were necessary to activate substrates in catalytic reactions. In another extreme of the spectrum, surface organometallic chemistry (SOMC), and, by extension, surface organometallic catalysis (SOMCat), have demonstrated that single atoms on a surface, but this time with specific ligands, could lead to a more predictive approach in heterogeneous catalysis. The predictive character of SOMCat was just the result of intuitive mechanisms derived from the elementary steps of molecular chemistry. This review article will compare the aspects of single atom catalysis and surface organometallic catalysis by considering several specific catalytic reactions, some of which exist for both fields, whereas others might see mutual overlap in the future. After a definition of both domains, a detailed approach of the methods, mostly modeling and spectroscopy, will be followed by a detailed analysis of catalytic reactions: hydrogenation, dehydrogenation, hydrogenolysis, oxidative dehydrogenation, alkane and cycloalkane metathesis, methane activation, metathetic oxidation, CO2 activation to cyclic carbonates, imine metathesis, and selective catalytic reduction (SCR) reactions. A prospective resulting from present knowledge is showing the emergence of a new discipline from the overlap between the two areas.