On Android:
They probably use Content Providers. As described in this link,
A content provider manages access to a central repository of data. A
provider is part of an Android application, which often provides its
own UI for working with the data. However, content providers are
primarily intended to be used by other applications, which access the
provider using a provider client object. Together, providers and
provider clients offer a consistent, standard interface to data that
also handles inter-process communication and secure data access.
A content provider coordinates access to the data storage layer in your application for a number of different APIs and components, these include:
- Sharing access to your application data with other applications;
- Sending data to a widget;
- Returning custom search suggestions for your application through the
search framework;
- Synchronizing application data with your server;
- Loading data in your UI.
TL;DR In short, Content Provider is a layer that allows you to share your database with other apps/widgets. So Google Probably has a Content Provider in every app which shares the accounts that have been used on this app.
On iOS:
Now I'm just an Android Developer, but after a quick Google Search, I found this post which talks about UIPasteBoard:
Use the UIPasteboard class to let a user to share data from one place
to another within your app, and from your app to other apps. For
sharing data with any other app, use the systemwide general
pasteboard; for sharing data with another app from your team—that has
the same team ID as the app to share from—use named pasteboards.
I can't assure you that this is exactly the way Google does it. But If I were to implement such thing across my apps, I would use this.
