Of course, you are confusing everyone by describing 'move a folder with pictures into a different folder'. As far as I can understand you, you want to either
Rename an existing folder leaving the existing folder files intact
Move files from one folder into another folder which already has files in it
Move a folder full of files as a whole into another folder (i.e. make it a subfolder)
Your intention might be the second option. In that case, how on earth do you expect 'the order of pictures' to remain the same?
You don't seem to be aware that in Windows explorer, the order of files is, by default, alphabetic, but you can decide on a folder by folder basis, to see then in a different order - that is one of the headings seen in list view. Which can be 20 or more different sequences.
Do this. In Windows explorer, click the 'view' menu option. Just over half-way down is an option 'Choose details...' and that opens a panel showing a huge list of details about the files that you can display, which you want to show in the details list, and the order you want to display them (as columns).
Once you have absorbed that, we'll come to how you see them sorted.....on one of those columns.....every time.