Development App Store and Normal App Store

There is only a single Apple App Store for each region. Some regions allow third party App Stores. While it is not recommended due to ability to compromise your security, you can install a Developer Certificate that allows an app to be downloaded from another source other than the Apple App Store. This is not something that can be done by accident as it requires your permission after reading the warning about security and the Certificate is visible at Settings > General > VPN & Device Management.

TT123B wrote:

I getting more and more frustrated with my simple task of getting my privacy back and also having my Apple Devices working properly.

Your desire for both privacy and for Google apps is an interesting choice, as Google is one of the largest advertisers, and is very fond of targeted tracking.

is there more than one App Store for IOS?

There are several potential (and pedantic) answers to that question, none of which seem relevant to your reported symptoms. (Pedantic? Each region has three different and potentially more app stores, each of the three for different purposes, and in some regions there are additional stores operated by third-party vendors. Not all apps are in all stores. And again, none of which seems even remotely relevant here.)

It seems strange that I downloaded the Google app the other day.

There is no one “Google app”. There are various Google apps, and apparently Google app bundles.

Then after restarting my phone the app had disappeared and under Apps on phone and not on device it wasn’t showing, ie blue cloud.

Enabling the offloading of unused apps can do that, particularly if you’re low on free local storage.

Details: Manage storage on iPhone - Apple Support

As for “Google app” discussions more generally, there can be alternatives to downloading and using various Google apps, too. Accessing Google Gmail from your iPhone, for instance, doesn’t need any Google apps installed.

Given ongoing questions about normal operations and behaviors, I’d tend to suggest not running developer or other betas. Particularly not with any devices you need to work, with any local data you need available and uncorrupted, and with any Apple Accounts and iCloud data you need available and uncorrupted and unconverted. We can’t help with betas around here, either. Not past helping to remove an installed beta.

Everyone can sign into the Developer Website using their Apple Account, you just wont have complete access for all features without purchasing a Developer Subscription.

To no longer receive beta updates, make sure you have turned off Beta Updates at Settings > General > Software Updates. You do not need to be a Developer in order to test public betas. In addition, to stop receiving emails or use the provided Feedback Assistant, then take the extra step to leave the program.

• To leave the Apple Beta Software Program, you must first sign in, then click the Leave Program link.

Apple Beta — Unenroll Your Devices

MrHoffman wrote:

Your desire for both privacy and for Google apps is an interesting choice, as Google is one of the largest advertisers, and is very fond of targeted tracking.

Agreed! Using any Google service and expecting Privacy is not going to happen.