Additive manufacturing (AM) of metal alloys using a laser as a machine tool is reaching levels of precision comparable to conventional processing methods. Stainless steel specimens fabricated by AM have been extensively evaluated in load-bearing applications, showing an adequate response concerning mechanical strength. However, research on wear behavior remains open to discussion. The present work evaluates the sliding wear response of 316L stainless steel fabricated by laser powder bed fusion in three conditions: (1) as-built, (2) stress-relieved at 550 °C, and (3) heat-treated at 1150 °C. A pin-on-disk tribometer and a nanoindentation tester were employed to assess the tribological response and compare it with the same cold drawing material. The wear track and volume loss were evaluated using a 3D surface profile meter. Furthermore, the finite element method was applied to validate the experimental results and obtain insights into the behavior of the pin and disk couple. The results show that the samples in the as-built condition exhibit higher wear resistance associated with higher hardness. Stress relief slightly alters the wear response, while heat treatment modifies the microstructure, reducing the sliding wear resistance. The wear of the heat-treated samples cannot be attributed to a single wear mechanism, a synergy between several sub-mechanisms, such as abrasion, adhesion, oxidation, and tribochemical reactions.