Alain-Degache There is more than dozen different possible dates in file metadata along with file attributes, so it is no wonder you are confused. Everyone is. That is why we do not expose all possible dates to the user in Tonfotos, and reduce it to only two - Creation and Modification. And we keep all this complexity to ourselves.
While it is more or less trivial with modification date, it is real challenge to decide what is actually correct photo taking date. Tonfotos has complicated priority list which date to prefer depending and what actually is available, if format is correct, and so on. For example, GPS date always has priority to everything else. That is why even if Phone clock is typically synchronized with cellular network, there is still possibility to set wrong manually, while GPS receives its time from satellites and that is why it is more trustworthy.
When you set the date using Tonfotos, it sets it in several places and sometimes deletes in others to avoid conflicts. To be specific, Tonfotos sets user dates into Exif fields DateTimeOriginal and OffsetTimeOriginal and also XMP field xap:CreateDate.
As to Windows, it is also not that simple. It does not just show specific metadata fields to you. It also has some its own mapping of the metadata fields into Windows fields, and it may depend on the file format and other factors. I think it is best to ask Microsoft what exactly mapping they have for the fields in the explorer.