@phil_1 While being an Adobe Creative Cloud subscriber gives you access to the full features of Acrobat Pro on desktop, and unlocks premium features within the mobile Acrobat Reader app, it does not remove the "contains ads" label on the Google Play Store (or Apple App Store) page for the basic Adobe Acrobat Reader mobile app.
The "contains ads" label on the app store is a disclosure that the free version of Adobe Acrobat Reader mobile may display ads or prompts for premium features (which can be considered a form of ad for their own products). Your Creative Cloud subscription, or an in-app purchase to upgrade the mobile app, unlocks the premium features and removes those specific prompts/ads for premium features within the app itself. However, the app store listing will still retain the "contains ads" label because the free, unsubscribed version inherently contains them.
You install the "same one that is on my Google Play download" because that is the correct app. Once you download it, you then need to log in to the Adobe Acrobat Reader mobile app with the Adobe ID associated with your Creative Cloud subscription. After logging in, the app should recognize your subscription and unlock the premium features, which includes removing the feature-specific advertisements or upgrade prompts.