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Site-specific evolutionary rates can be estimated from codon sequences or from amino-acid sequences. For codon sequences, the most popular methods use some variation of the dN/dS ratio. For amino-acid sequences, one widely-used method is called Rate4Site, and it assigns a relative conservation score to each site in an alignment. How site-wise dN/dS values relate to Rate4Site scores is not known. Here we elucidate the relationship between these two rate measurements. We simulate sequences with known dN/dS, using either dN/dS models or mutation--selection models for simulation. We then infer Rate4Site scores on the simulated alignments, and we compare those scores to either true or inferred dN/dS values on the same alignments. We find that Rate4Site scores generally correlate well with true dN/dS, and the correlation strengths increase in alignments with higher sequence divergence and higher number of taxa. Moreover, Rate4Site scores correlate nearly perfectly with inferred dN/dS values, even for small alignments with little divergence. Finally, we verify this relationship between Rate4Site and dN/dS in a variety of natural sequence alignments. We conclude that codon-level and amino-acid-level analysis frameworks are directly comparable and yield near-identical inferences.