In Affinity Designer all edits you make are saved in the document history, not just for the current session but for any subsequent session too. You can also save your project as an .afdesign file at any time. Where this file will be written to depends on whether you have imported an image or opened an image "in place".
Affinity Designer's Home screen acts much like a series of "tabbed" documents you would typically find in the desktop version. All documents are stored internally as part of the app's storage, but you can also save them out. If you have opened a file "in place" (e.g. from cloud storage), the document will be saved back to that file. If you have imported a file, and thus created a copy, the document will be saved to either local iPad storage ("On My iPad") or to iCloud Storage (in a directory named "Affinity Designer") where you can easily access them. The choice of save location is determined by the Preferences option.
If you have imported a RAW image or an image from your Apple Photos library, a saved Untitled document will always be created. For other imported documents (e.g. .afdesign or image files), the existing filename will be used.
If you need to undo your work at any time, you can use the History Studio to scroll back to a history step from which to begin editing again; history steps subsequent to this step will be replaced by your new editing steps.
If your document is newly created, you may like to rename it from 'Untitled' to something more meaningful and memorable.
To rename an Untitled document:
From Affinity Designer's Home screen, tap the menu icon at the bottom right of the saved document's thumbnail.
On the pop-up menu, tap Rename.
To save your document:
From Affinity Designer's Home screen, tap the menu icon at the bottom right of the saved document's thumbnail.
On the pop-up menu, tap Save.
To close your document:
If you wish to keep your work, ensure you have saved the document first by using the Save option.
From Affinity Designer's Home screen, tap the menu icon at the bottom right of the saved document's thumbnail.
On the pop-up menu, tap Close.
To save a copy of your document (from workspace):
From the Document Menu, select Save a Copy.
(Optional) Enable Save history if you want the history to be retained in the copy.
Enter a new file name for the copy.
Tap Save.
Choose your desired cloud storage and (optionally) a directory to save the document to.
To save a copy of your document (from workspace):