Hi @adam,
Long time no see! 
Folders are way to structure and categorize your data better.
Say that your board is your design agency.
Now, in a design agency there could be multiple departments: animation, video, and images (or UX/UI).
Folders are exactly that: units which will help you classify your organization better, and have a better look at your board.
Folder A — Animation
Folder B — Video
Folder C — Images
—
On the other hand, views (or Tabs) are simply another / an additional way to see and organize your data. THE SAME data.
So, in folder A, there’s a certain data. (Say account credentials for your business). You can have three different views (A, B, C) organized in different views - such as columns, list and calendar, also grouped by different attributes, or with another filter applied. Possibilities are endless.
In folder B, there’s another type of data (like your employee’s info). Now in that specific folder, you can also have 2 different views, such as Table and List with, yet again, different setup (group, filter, sort, etc).
—
- Can an item exist in more than one folder? (I can’t figure out how to see the same item two folders at once.)
It can. You can now duplicate an item if you expand it, and click on the three dots, and drag&drop the duplicated item to another folder.
An option to ‘Move’ or ‘Move and Merge’ option will show. I suggest going with Move & Merge 
Hope this was helpful.
Also, maybe we can try talking this through over Skype, or a Demo. Feel free to schedule it here: https://calendly.com/startinfinity