iOS (and Mac) has what Apple call a 'saveless' model. Your maps are saved automatically every minute or so and each time you switch away from the app (or turn off the screen.) There is no need (or mechanism) to specifically save a map. This can be odd at first (if you’re used to Windows) - but it does 'just work' :-)
NB: It is important that you do NOT kill the app immediately after you’ve finished with it - it might be in the process of saving some changes.
To save your maps somewhere other than iCloud or locally on your device (eg Dropbox or OneDrive) you will need to install the cloud provider app then enable it in the ‘Locations’ section (left side bar) in the iThoughts document picker.
NB: If you want to save to a WebDAV server or somewhere like Drive or Amazon then you could try installing the FileBrowser app.
Like it's iOS counterpart, the Mac app has a 'saveless' model. Changes are automatically and continuously saved (to disk.) There is no need to specifically select File -> Save.
This is great and it means that you should never lose any work (due to crashes or forgetting to save a document.)
For Windows users (used to specifically saving documents) this can appear 'odd' and sometimes 'annoying'. On Windows, you might open a document, make some changes, decide better of it and close the document - choosing not to save changes. This will not work on the Mac - changes are always saved (whether you want to keep them or not.) Another time this approach can be confusing/annoying is when you open a template document, make some changes and then attempt Save As - only to find that there is no Save As option and that your changes have instead been automatically saved back into the template.
There are 2 things to know here:
Save As is possible - hold down the option (⌥) key whilst opening the file menu.
macOS comes with a feature called Versions where a version history is maintained for all documents. This enables you to revert to a previous version of a document using a Time Machine style interface. See File -> Revert To menu.
By default the Windows app follows the 'standard' Windows approach to saving files. That is to say, a document is NOT automatically saved. The user will be prompted to save any changes when they attempt to close the document.
This is not great if the app crashes (your changes will not have been saved!) To assist with this, iThoughts will periodically save a copy of the document in the background (giving it a ~itmz~ file extension.) If the app crashes then next time the document is opened it will tell you that there were unsaved changes to the document and ask if you want to recover them. You probably DO want to do this. Either way, the backup copy is then deleted (so you only get one chance to decide!)
There is an option in the Help-> Settings called Auto Save. If this is enabled, then the document is automatically saved (every minute or so and each time you switch away from the app.) This makes it behave much more like the iOS/Mac versions - and it means you can forget about saving and crashing etc.
NB: There is a downside to Auto Save. Many people will open a document, make a bunch of changes then decide to save them to a new document (using Save As.) This normally results in the original document being unchanged. However, when auto save is enabled, this is NOT the case. In this situation the best approach is to make a copy of the original document and edit that (rather than attempting to use Save As with Auto Save)