Why do I have Termux and Termux(failsafe)? Why do I have two Termux applications, and what's the difference? This happened recently, after updating Termux I believe. I've installed Termux from F-Droid, and it mentions (failsafe) in the application name there. Cannnot see that in the Play Store.
Termux (failsafe) is shown on the app drawer since the last update. When you update Termux to the latest version, it is also shown.
From this comment from what is Termux (failsafe)?:

We have made sessions auto-closeable, see #988 for more information.
Auto-closeable sessions may put application into &quot;denial-of-service&quot; condition if user will mess with files like .bashrc - in such case access to files on internal storage will be completely lost. Thus we had to create a separate icon.
It's very unlikely that we will remove it. Easy access to failsafe shell is mandatory but unfortunately there no other reliable variants that will work on all Android versions.

Also based in this comment in Termux github:

This creates a limited shell using only the Android system tools.

If for whatever reason Termux is unable to start, then use Termux failsafe.