Until now, if you wanted to install Telegram on an Android mobile, the normal thing was to go to Google Play and press the install button. Now, Telegram offers the APK of your application on your website, and it is not exactly the same version available on Google Play.
Telegram now has a version of Google Play and a different one, accessible from the APK. The version is slightly different (7.6.0 on Google Play and 7.7.0 the APK) but they also differ in that the APK has fewer restrictions and it updates automatically, without going through the Google store.
Normal version and APK version
All applications available on Google Play must comply with Google's standards, both those that determine the applications that have a place or not in the store and those that restrict applications that require special access, such as accessibility or access to SMS and calls, as well as the obligation to use Google's own payment system.
If an Android application does not want to be subject to Google's demands, it must find another way to distribute it outside of its store, and that is exactly what Telegram has done. It is not an all or nothing approach, like Epic with Fortnite, but Telegram has two versions: that of Google Play and that of its APK, accessible from the app's website.
As specified by Telegram on its website, the version accessible from the APK "has fewer restrictions and receives automatic updates from telegram.org", although it is not clear what restrictions are avoided with the Telegram APK.
These restrictions could be related to the moderation and adult content policy of some channels and groups, a problem that Discord may have experienced with its presence in the App Store, or perhaps with the payment systems policy, in case the application is preparing its own system. At the moment, both versions are almost indistinguishable, so that it is not clear what has changed.
Telegram is neither the first nor the last application to have one version for Google Play and another, without limits, outside the store. Another famous example is the call recording application ACR, whose Unchained version (without strings) allows recordings to obtain the number of who is calling, something not possible with the Google Play version that must follow Google's rules on access to SMS and calls.