Accidental Formatting
Formatting a drive looks and feels like a wipe, but in most cases it does something surprisingly similar to deleting every file at once, leaving the actual data largely intact underneath a fresh, empty-looking file system.
What's actually happening
A "quick format" writes a new, empty file system structure — a fresh index, a fresh boot sector — without touching the area of the disk where file data actually lives. A "full format," despite the name, generally doesn't zero out that data either on modern Windows and macOS; since Windows Vista, a full format mostly adds a bad-sector scan on top of the same quick-format behavior, and it only overwrites data if an explicit low-level wipe option is chosen. In practice, most accidental formats — quick or full — leave the file data itself sitting where it was.
How recoverable this really is
Often good, with one honest caveat that makes this different from plain deletion: the new, empty file system's own metadata frequently gets written to the exact same fixed on-disk locations the old file system's metadata used — the start of the drive, for instance. So while file contents usually survive, the old directory structure describing names and folder paths is often the first thing lost, even when the files themselves are fully recoverable.
The general approach
If a backup copy of the old file system's index partially survived the format — which happens more often than people expect, especially with a quick format that reused the same file system type — recovery software can sometimes rebuild the original folder structure and names directly from it. Where that's gone, the fallback is the same signature-based carving used for plain deletion: scanning the raw disk for recognizable file headers, which recovers content reliably but generally without the original names.
Don't format the drive again "to see if that fixes it," and don't save anything new to it while deciding what to do next. A second format is one of the more common ways this situation goes from recoverable to not, because it gives the new file system's metadata a second chance to land on top of whatever survived the first time.
Practical, step-by-step guides for specific recovery software will be added here as separate linked articles.
This page describes the general situation, not a guaranteed fix for your specific case. If you'd rather have someone experienced take a look before you try anything, see what a hands-on evaluation looks like.