That probably happens because your hard disk is formatted NTFS and your USB-stick is formatted FAT32.

I don't think it harms, but why not try? Just copy one picture to the USB-stick, copy it back to another location on your hard disk and compare the original and the copy. What do you see?

If unhappy with the result, change the USB-stick to NTFS and everything will be fine. But you can't use it in your Mac then anymore. Or use another USB-stick or an external drive, that already is NTFS.

By the way, do I understand correctly you don't yet have a backup? Then you are lucky you didn't lose those pictures already in the past. Better start a regular backup for things you don't want to lose.

Kees