Liver steatosis is a frequent finding in clinical practice and it is estimated to affect 30% of the general adult population worldwide. It became one of the leading causes of end-stage liver disease and hepatocellular carcinoma. From its first description, a diagnosis of nonalcoholic fatty liver disease (NAFLD) required the exclusion of excessive alcohol consumption and concomitant chronic liver diseases of different origins, making it a diagnosis of exclusion. In recent years, the need to stress the strict association between liver steatosis and metabolic dysfunction (i.e., insulin resistance, overweight/obesity, type 2 diabetes, and metabolic syndrome), as well as the desire to define a condition in a positive rather than negative way, led to new definitions and new diagnostic criteria. Metabolic dysfunction-associated fatty liver disease (MAFLD) was proposed by Eslam et al. in 2020. More recently, a Delphi consensus endorsed by several international hepatologic societies proposed a new terminology [metabolic dysfunction-associated steatotic liver disease (MASLD)] and a new set of diagnostic criteria. The MAFLD and MASLD definitions have a good degree of concordance. They mainly differ in the number of metabolic derangements needed to define “metabolic dysfunction” in normal-weight individuals and in alcohol consumption. Indeed, while MAFLD does not exclude patients with significant alcohol consumption, the recent Delphi consensus included the metabolic dysfunction and alcohol-related liver disease (MetALD) disease entity, a condition in which steatosis, metabolic dysfunction, and moderate alcohol intake coexist. In the present narrative review, we underline the strengths and possible limitations of each definition and summarize available evidence from epidemiologic studies evaluating the clinical usefulness of each set of diagnostic criteria.