Difference between androidx and com.android.support
All the support libraries are dropping the v4 v7 v12 v13 etc tags and everything is refactored into the androidx packages.
They are essentially the same but for future reference androidx will be the library that we should use in our apps.
Android studio 3.2 canary that comes out this week (week of May 14, 2018) should have the tool that allows automatic refactoring to the androidx packages. There was an announcement about this at google i/o 2018.
One of the difference between AndroidX and Support libraries is that when you use support libraries, all support libraries must be the same version, but in androidX there is no such thing.
other thing is that in support library, most of the time when you need a component in your app, you have to add dependencies that have so many other thing that you really don't need. but in AndroidX you can add only the dependency that you need and no more.