Q: Wifi syncs between iPad and iPhone, want it to stop

WiFi sync has nothing to do with it. This is normal behavior when signed into multiple devices using the same iCloud account. If you don't want your phone on the WiFi network at work, turn off WiFi when you're there.

What am I missing? FWIW I don't consider your experience normal behavior. To be sure I decided to do a test. I am at home and my iPad and iPhone are on the same network and using the same iCloud account. I forgot the network on my iPhone and it reverted to LTE. However my iPad remained logged in with no issues, essentially what you want.

First try a Forced Restart. Hold down the Home and Wake/Sleep buttons at the same time for about 15 seconds until the Apple logo appears. You will not lose anything.

The reset your network settings on both devices. Settings > General > Reset > Reset Network Settings. Note that this will forget all previously entered Wi-Fi passwords.

Then rejoin the work network on your iPad but not on your iPhone.

It's been like this at least since iOS 9 and El-Cap were released, possibly earlier (I'm old and my memory doesn't work as well as it used to). WiFi settings are synced between all iOS and OS X devices signed into the same iCloud account. Join a network on one, and all other devices will get the settings synchronized to it automagically. Delete it, and it will be deleted from all. Perhaps you're just seeing a delay in synchronization.

Tim, I cannot explain the difference (I am old also).

I tried it again, forgot my home network on my iPhone and the iPad (wifi only, not on phone's hotspot, but using same iCloud account) is still connected to the home wifi 20 minutes later. I just did a speedtest with it, all ok. Maybe it takes longer to sync so I will leave it as-is for a bit. However I would be surprised if it disconnected. I have a dual band router and I used to run both devices on the 2.4 band to get longer range. Some months back I forgot the 2.4 network on my iPhone and started using the 5 GHz band so I could use OOKLA and test speeds on each. I did not disconnect from the 2.4 on my iPhone, I forgot it so it would not connect automatically, and the iPad remains connected to the 2.4 even after months.

Out of curiosity, would you test yours?

If you have not found a solution to your issue, check your Settings for iCloud Keychain. You may have to turn it off as it could be syncing your Wi-Fi networks.

Frequently asked questions about iCloud Keychain - Apple Support