If the app is deployed from Google Play (aka, I is not a custom written app) it should be updated automatically. I don't think you can even stop the updates.
It works exactly the same on Android as it does on iOS.
Some gotchas to keep an eye out for:
Some manufacturers configure their devices to only update over WiFi by default. If you have mobile data only connected device this stops updates.
You need to use Device Owner mode to be assured the update will push out. In BYOD mode it is more like asking the device "pretty please" to upgrade.
Devices may apply additional state tests when deciding to do an update. For example, they may decide not to do updates when the battery is less than 80%. This is manufacturer dependent.
If the app is deployed from Google Play (aka, I is not a custom written app) it should be updated automatically. I don't think you can even stop the updates.