The progress continues in any of these versions - game just upgrade older save.
Regarding difference between android and android HD version, in short there are 2K and 4K textures used in HD version which is tricky to ensure it works on all android devices in general, on some it works on some it may crash due to low RAM or act very slow or run without any issues. Hard to predict, impossible to fix as not all smartphones are not used to work with such high quality of textures.