Expanding on what Pingaware said, yes the problem stemmed from the fact that you, probably inadvertently, enabled the "auto-organise media files" option. What that option does is, it automatically organizes your files based on a naming template defined in its settings, which is what happened in your case. I highly advice against enabling that option unless your whole library is correctly tagged, which yours is not, and you are 100% percent sure about what you are doing. So for now you need to disable that option.
From your screenshot of where the files were originally, it is evident to me that it will be virtually impossible to return the files in the exact same manner they were originally before being moved. The reason for this is, there was no coherent folder and naming structure that the folders/files followed. You probably placed them there unaltered from various sources, am I right?
The good news are, now you get the chance to actually structure your files in a far better way than it was before. This can be achieved very easily with tools already available within MusicBee but will require some work and time on your part depending on the size of your library. I can see that your library is not that big, from the screenshots your provided, so it's not going to take too long to get everything sorted once you get the hang of it.
Now let's get started. What you definitely want to do first is to make sure that everything is tagged correctly. This may or may not prove to be complicated depending on how badly tagged your tracks already are.
Here are some basic guidelines:
1. I recommend that you change the view to "Album and Tracks" as I find that it is visually the most coherent to get some tagging work done. To change to this view press the "Configure Layout" button which is located right next to the search bar.
2. Change the sorting to something sensible like Album Artist/Year (right-click on a column header to change it)
3. I suggest you select everything and drag and drop it to the "Inbox" node found in the left sidebar and only drag and drop back to the library anything that has been tagged correctly. This is basically the main use of the Inbox node, it provides a way to listen, edit, tag and organize files before they meet a certain standard and are allowed to enter your library. Note that moving files between Inbox/Library does NOT physically move the files, it all happens visually within MusicBee.
3. Right-clicking on an album art in the main view will select the whole album and you can also choose to "Auto-tag by Album" from the context menu. In the dialog that opens as long as you are able to input the correct album name and album artist you will almost definitely get a good result provided that the selection is an actual release. You can probably figure out the rest from there as the interface is kinda self explanatory.
4. For tracks that are missing tags entirely (or missing an album tag), you can either right-click>auto-tag by track and choose "identify track and update tags" which will try to retrieve tags based on a sound signature of the file but is hit or miss sometimes or you can more optimally use the "infer tags from filename" given that the filename is something sensible. In your case there will probably be many track whose filename might not make much sense since you have already changed it based on the tags.
5. Ignore retrieving album artwork for now, as it's better to perform it once your files are well organized depending on whether you choose to save the artwork inside the files or inside a folder.
6. You may probably need to use google for extreme cases where no correct tags can be retrieved and use your wits to figure it out
That's all for now, once you are done with tagging you can move on to organizing the files into folders. Just let me know when you are done and feel that everything is tagged correctly.
If you need any help feel free to ask here. I may even be able to help you remotely with a utility like Teamviewer if you hit a dead end, just drop me a PM.