Understanding the Diversity of 21 cm Cosmology Analyses

21 cm power spectrum observations have the potential to revolutionize our understanding of the Epoch of Reionization and Dark Energy, but require extraordinarily precise data analysis methods to separate the cosmological signal from the astrophysical and instrumental contaminants. This analysis challenge has led to a diversity of proposed analyses, including delay spectra, imaging power spectra, m-mode analysis, and numerous others. This diversity of approach is a strength, but has also led to confusion within the community about whether insights gleaned by one group are applicable to teams working in different analysis frameworks. In this paper we show that all existing analysis proposals can be classified into two distinct families based on whether they estimate the power spectrum of the measured or reconstructed sky. This subtle difference in the statistical question posed largely determines the susceptibility of the analyses to foreground emission and calibration errors, and ultimately the science different analyses can pursue. In this paper we detail the origin of the two analysis families, categorize the analyses being actively developed, and explore their relative sensitivities to foreground contamination and calibration errors.