Would you choose as a notification message displayed to a user on a website "your messages have been successfully moved to trash" or "... the trash"?
What is the difference and which one is more accurate?
In a very short-format setting, such as the label to an icon, "move to trash" would be acceptable. It's not grammatically perfect, but the need for brevity makes it acceptable.
For a longer form setting, such as the full sentences you'd find in a dialog box, I'd use the more grammatically acceptable "..moved to the trash" (or the more politically correct, "moved to the recycle bin".)