We fit various colour-magnitude diagrams (CMDs) of the Galactic globular clusters NGC 6397 and NGC 6809 (M55) by isochrones from the Dartmouth Stellar Evolution Database (DSED) and Bag of Stellar Tracks and Isochrones (BaSTI) for α-enhanced [α/Fe] = +0.4. For the CMDs, we use data sets from Hubble Space Telescope, Gaia, Visible and Infrared Survey Telescope for Astronomy, and other sources utilizing 32 and 23 photometric filters for NGC 6397 and NGC 6809, respectively, from the ultraviolet to mid-infrared. We obtain the following characteristics for NGC 6397 and NGC 6809, respectively: metallicities [Fe/H] = -1.84 ± 0.02 ± 0.1 and -1.78 ± 0.02 ± 0.1 (statistic and systematic uncertainties); distances 2.45 ± 0.02 ± 0.06 and 5.24 ± 0.02 ± 0.18 kpc; ages 12.9 ± 0.1 ± 0.8 and 13.0 ± 0.1 ± 0.8 Gyr; reddenings E(B - V) = 0.178 ± 0.006 ± 0.01 and 0.118 ± 0.004 ± 0.01 mag; extinctions AV = 0.59 ± 0.01 ± 0.02 and 0.37 ± 0.01 ± 0.04 mag; and extinction-to-reddening ratio RV=3.32+0.32−0.28 and 3.16+0.66−0.56. Our estimates agree with most estimates from the literature. BaSTI gives systematically higher [Fe/H] and lower reddenings than DSED. Despite nearly the same metallicity, age, and helium enrichment, these clusters show a considerable horizontal branch (HB) morphology difference, which must therefore be described by another parameter. This parameter must predominantly explain why the least massive HB stars (0.58-0.63 solar masses) are only found within NGC 6809. Probably they have been lost by the core-collapse cluster NGC 6397 during its dynamical evolution and mass segregation. In contrast, NGC 6809 has a very low central concentration and, hence, did not undergo this process.