Where do deleted files go?

I need to make more storage room on my iPad, so am deleting a lot of old paintings from the gallery.
Are these permanently removed from the iPad? Or do they linger somewhere still taking up space?
I really want to remove them permanently and not have them cached somewhere.
Any tips for clean removal of unwanted paintings?

Strictly speaking deleted files don’t go anywhere.
What happens after deleting a file is that the “space” it occupied is now marked by the system as free for other things to be written there.
So they are there but not there taking up valuable space.
Eventually the data blocks that made up the file/s will be overwritten with new data, maybe not all at once, but eventually all of the blocks of data that made up the deleted file/s will be used and then the file/s will be truly gone.

Thanks, Mark, for that prompt and clear explanation. It is a great help.