// what these tools actually doTwo operations. That is the whole category.
Understanding this helps explain the differences between tools.
There are two main actions to restore data. Every recovery product, whether you pay for it or use the free version will either perform one action or both.
Reading file system structures. The software uses what's left on the drive where you had the data when you can still read what was originally written, as with a deleted file or a lost partition. The "map" was used by the operating system as an index so it could find everything. It builds this again once it has enough information about what the original map looked like, which allows your files to be returned with their names and the same folder structure that you were using before. And that is much better.
Carving by signature. When the index does not exist any more, the software searches through the raw disk for bytes that represent common file types — such as JPEG, DOCX, PDF, MP4 — and builds each back up from its beginning (header), but no names or folders are assigned to these files since those existed in the index.
While different software programs vary greatly in the number of file signatures they recognise, how well they work with APFS containers or LVM pools — and how well they look while being run — there is no difference in physics.