iOs 13

For updating apps you go to the App Store, tap your thumbnail/picture in the upper right corner and choose the apps at the bottom of the screen you’d like to update (or press the blue Update all-link).

Syncing your phone to a Mac is basically the same as before: use the USB-to-lightning cable to connect your phone to your Mac, open iTunes, click your phone from within iTunes and press sync.

Even older than iOS 13 and iTunes syncing things to a Mac.

To update apps on an iOS device you use the App Store but a bit different method:

https://www.cnet.com/how-to/your-iphones-apps-dont-update-the-same-in-ios-13-heres-what-to-do-now/

You can't run an iOS apps on a Mac.

iTunes on the computer can be used to do a iOS backup or restore and download updates and upgrades.