Play store is part of Google Play

Yes, that is completely correct. The Play Store is the primary app delivery component within the larger Google Play ecosystem. [1]

Why this relationship works

• The Store is a portal: The Play Store app serves as your digital gateway into the broader Google Play marketplace.
• The parent brand provides infrastructure: Google Play handles your payment profiles, security scanning (via Play Protect), and cloud library syncing across all your devices. [2, 3, 4, 5, 6]

If you want to explore further, let me know if you would like to look into how Google Play Protect secures your downloads, or how to manage your Google Play Library across different devices.

[1] https://www.alexomegapy.com

[2] https://www.mobiletopup.co.uk

[3] https://www.csmonitor.com

[4] https://support.google.com

[5] https://www.meelio.ai

[6] https://android-developers.googleblog.com