One of Gmail's "innovations" was to abandon the traditional hierarchical folder model. In Gmail, you don't move or copy messages to folders -- you give them labels. The labels themselves can be hierarchical, but the big difference is that one individual message can have more than one label. If you think of labels as folders, this means that a message can exist in more than one folder. Another one of Gmail's departures from conventional email is archiving, which takes a message out of view, but leaves it available for search. I was never quite sure over the years how, but frequently Gmail would archive a message when I didn't intend it. If I didn't know what to search for, it was gone.
Now that I'm back on a classic folder model I'm much happier and everything seems logical. I can still search and find anything I want and messages no longer disappear mysteriously. Outlook's auto-archiving feature, moves items to a PST file, is clumsy compared to Gmail's, but it's much more flexible, and there are many third-party products to assist with Exchange search and archiving.