We present high-definition observations with the James Webb Space Telescope (JWST) of >1000 Cepheids in a geometric anchor of the distance ladder, NGC 4258, and in five hosts of eight Type Ia supernovae, a far greater sample than previous studies with JWST. These galaxies individually contain the largest samples of Cepheids, an average of >150 each, producing the strongest statistical comparison to those previously measured with the Hubble Space Telescope (HST) in the near-infrared (NIR). They also span the distance range of those used to determine the Hubble constant with HST, allowing us to search for a distance-dependent bias in HST measurements. The superior resolution of JWST negates crowding noise, the largest source of variance in the NIR Cepheid period-luminosity relations (Leavitt laws) measured with HST. Together with the use of two epochs to constrain Cepheid phases and three filters to remove reddening, we reduce the dispersion in the Cepheid P-L relations by a factor of 2.5. We find no significant difference in the mean distance measurements determined from HST and JWST, with a formal difference of -0.01 +/- 0.03 mag. This result is independent of zero-points and analysis variants including metallicity dependence, local crowding, choice of filters, and slope of the relations. We can reject the hypothesis of unrecognized crowding of Cepheid photometry from HST that grows with distance as the cause of the "Hubble tension" at 8.2 sigma, i.e., greater confidence than that of the Hubble tension itself. We conclude that errors in photometric measurements of Cepheids across the distance ladder do not significantly contribute to the tension.