To assess the potential environmental impact of human/industrial systems, life cycle assessment (LCA) is a very common method. There are two prominent types of LCA, namely attributional (ALCA) and consequential (CLCA). A lot of literature covers these approaches, but a general consensus on what they represent and an overview of all their differences seems lacking, nor has every prominent feature been fully explored. The two main objectives of this article are: (1) to argue for and select definitions for each concept and (2) specify all conceptual characteristics (including translation into modelling restrictions), re-evaluating and going beyond findings in the state of the art. For the first objective, mainly because the validity of interpretation of a term is also a matter of consensus, we argue the selection of definitions present in the 2011 UNEP-SETAC report. ALCA attributes a share of the potential environmental impact of the world to a product life cycle, while CLCA assesses the environmental consequences of a decision (e.g., increase of product demand). Regarding the second objective, the product system in ALCA constitutes all processes that are linked by physical, energy flows or services. Because of the requirement of additivity for ALCA, a double-counting check needs to be executed, modelling is restricted (e.g., guaranteed through linearity) and partitioning of multifunctional processes is systematically needed (for evaluation per single product). The latter matters also hold in a similar manner for the impact assessment, which is commonly overlooked. CLCA, is completely consequential and there is no limitation regarding what a modelling framework should entail, with the coverage of co-products through substitution being just one approach and not the only one (e.g., additional consumption is possible). Both ALCA and CLCA can be considered over any time span (past, present & future) and either using a reference environment or different scenarios. Furthermore, both ALCA and CLCA could be specific for average or marginal (small) products or decisions, and further datasets. These findings also hold for life cycle sustainability assessment.