Course-based undergraduate research experiences (CUREs) are tools used to introduce students to authentic participation in science. Several specific CUREs have been shown to benefit students' interest and retention in the biological sciences. Nevertheless, CUREs vary greatly in terms of their context, methodology, and degree of research authenticity, so different types of CUREs may differently influence student outcomes. This programmatic diversity poses a challenge to educators who want to better understand which course components and features are reliably present in a CURE curriculum. To address these issues, we identified, catalogued, and classified 112 potential features of CUREs across the biosciences. To develop the list, we interviewed instructors experienced with teaching individual and large networked CUREs across a diversity of the biological disciplines, including: Squirrel-Net (field-based animal behavior), SEA-PHAGES (wet lab microbiology and computational microbiology), Tiny Earth (environmental and wet lab microbiology), PARE (environmental microbiology), and the Genomics Education Partnership (eukaryotic computational biology). Twenty-five interviewees contributed expert content in terms of CURE features and classification of those items into an organized list. The resulting list's categories encompasses student experiences with the following: (i) the scientific process; (ii) technical aspects of science; (iii) the professional development associated with research; and (iv) building scientific identity. The most striking insight was that CUREs vary widely in terms of which features they contain, since different CUREs will by necessity have different approaches to science and student involvement. We also identified several features commonly thought to be crucial to CUREs yet have ambiguous definitions. This ambiguity can potentially confound efforts to make CUREs research-authentic and aligned with the central goals of science. We disambiguate these terms and represent their varied meanings throughout the classification. We also provide instructor-friendly supplementary worksheets along with considerations for instructors interested in expanding their CURE course design, instruction, and equity.