Are the Achievements the same on Steam and mobile?

Steam and mobile achievements will not retroactively unlock when you next login to your iOS, Android or Amazon device.

Instead, the game checks when a related action occurs when you login to a different platform and will complete the task then.

For example, owning 100 unique troops can be unlocked on Steam, and when playing on Android, if you get your 101st troop, then you will receive that achievement on Android as well. 

But if you have achievements that can only be completed once (such as 'Student'), these may not be triggered again, so some achievements will not be unlocked on your second device.