  We use the IllustrisTNG cosmological hydrodynamical simulation to study the
formation of ultra-diffuse galaxies (UDGs) in galaxy clusters. We supplement
the simulations with a realistic mass-size relation for galaxies at the time of
infall into the cluster, as well as an analytical model to describe the
tidally-induced evolution of their stellar mass, velocity dispersion and size.
The model assumes "cuspy" NFW halos and, contrary to recent claims, has no
difficulty reproducing the observed number of UDGs in clusters. Our results
further suggest that the UDG population consists of a mixture of "normal" low
surface brightness galaxies such as those found in the field ("born" UDGs, or
B-UDGs), as well as a distinct population that owe their large size and low
surface brightness to the effects of cluster tides ("tidal", or T-UDGs). The
simulations indicate that T-UDGs entered the cluster earlier and should be more
prevalent than B-UDGs near the cluster centres. T-UDGs should also have, at
given stellar mass, lower velocity dispersion, higher metallicities, and lower
dark matter content than B-UDGs. Our results suggest that systems like DF-44
are consistent with having been born as UDGs, while others such as DF2, DF4 and
VLSB-D are possibly extreme T-UDG examples.
