IMO they're different designations for what's meant to be the same ship. In real life, they just made a model with more detail.
Voyager explicitly called a K'tinga-class ship a D7 in "Prophecy". The undetailed D7 was given the same patterning as the K'tinga in "Trials and Tribble-ations" and TOS-Remastered's new CG.
Saying they're different classes is like insisting Saavik underwent extensive plastic surgery between STII and III to explain away her recasting.