Aurora Store is same as Play Store
Overall, Aurora Store is an intriguing app, that completes two functions. First of all, it makes it easy to download virtually any APK offered on Google Play, and second, it enables you to manage the apps already on your device. All from an elegant, intuitive interface.
This makes it clear that the source for Aurora is Play Store. Also the FAQ has this
Is it safe to use Aurora store?
Aurora Store is fully open-source and verified by F-Droid. If you're asking about the safety of the apps in the store, those are the exact same ones the Play Store would load and display. A lot of dangerous stuff seems to sneak past Google though, so as a rule of thumb, don't download anything which you're unsure about.
Why does Aurora show more updates than Play Store?
New and existing users are eligible to receive updates from staged rollouts and are chosen at random for each new release rollout.
Your app update will be available to the percentage of users in your staged rollout, but it may take time for the full group to receive the update.
Users won't be notified if they receive a version of your app in a staged rollout.
If you choose specific countries for your staged rollout, the upgrade will be limited to users with Google Play accounts in those locations.
Robert's answer gives additional reasons for staged rollouts
To summarize, you won't see all app updates available on Play Store
Aurora Store is legitimate
The updates in Aurora are legitimate Aurora store is open source hosted on Github and the latest update to readme says
The source code for Aurora Store is actively developed on GitLab. You can find the latest updates, contribute to development, and track the progress on the Aurora Store GitLab repository
Hence, there is no reason at all to doubt the authenticity of Aurora Store. As a side note the developer of Aurora store is also the developer of Warden which is a tool for privacy conscious users, since
Detects Trackers & Loggers across whole device
Allows to disable all trackers/logger