  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
$\alpha$-enhanced [$\alpha$/Fe]$=+0.4$. For the CMDs, we use data sets from
{\it HST}, {\it Gaia}, VISTA, 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]$=-1.84\pm0.02\pm0.1$ and
$-1.78\pm0.02\pm0.1$ (statistic and systematic uncertainties); distances
$2.45\pm0.02\pm0.06$ and $5.24\pm0.02\pm0.18$ kpc; ages $12.9\pm0.1\pm0.8$ and
$13.0\pm0.1\pm0.8$ Gyr; reddenings $E(B-V)=0.178\pm0.006\pm0.01$ and
$0.118\pm0.004\pm0.01$ mag; extinctions $A_\mathrm{V}=0.59\pm0.01\pm0.02$ and
$0.37\pm0.01\pm0.04$ mag; extinction-to-reddening ratio
$R_\mathrm{V}=3.32^{+0.32}_{-0.28}$ 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.
