Standardized terminology in science is important for clarity of interpretation and communication. In invasion science — a dynamic and quickly evolving discipline — the rapid proliferation of technical terminology has lacked a standardized framework for its language development. The result is a convoluted and inconsistent usage of terminology, with various discrepancies in descriptions of damages and interventions. A standardized framework is therefore needed for a clear, universally applicable, and consistent terminology to promote more effective communication across researchers, stakeholders, and policymakers. Inconsistencies in terminology stem from the exponential increase in scientific publications on the patterns and processes of biological invasions authored by experts from various disciplines and countries since the 1990s, as well as publications by legislators and policymakers focusing on practical applications, regulations, and management of resources. Aligning and standardizing terminology across stakeholders remains a prevailing challenge in invasion science. Here, we review and evaluate the multiple terms used in invasion science (e.g. 'non-native', 'alien', 'invasive' or 'invader', 'exotic', 'non-indigenous', 'naturalized, 'pest') to propose a more simplified and standardized terminology. The streamlined framework we propose and translate into 28 other languages is based on the terms (i) 'non-native', denoting species transported beyond their natural biogeographic range, (ii) 'established non-native', i.e. those non-native species that have established self-sustaining populations in their new location(s) in the wild, and (iii) 'invasive non-native' — populations of established non-native species that have recently spread or are spreading rapidly in their invaded range actively or passively with or without human mediation. We also highlight the importance of conceptualizing 'spread' for classifying invasiveness and 'impact' for management. Finally, we propose a protocol for classifying populations based on (1) dispersal mechanism, (2) species origin, (3) population status, and (4) impact. Collectively and without introducing new terminology, the framework that we present aims to facilitate effective communication and collaboration in invasion science and management of non-native species.