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 50 unique pieces of Gear can be unlocked on Steam, and when playing on Android, if you get your 51st troop, then you will receive that achievement on Android as well. 

in-gameYou can also force trigger some Goals in game that you may have already collected on another crossplay platform by tapping on the Goal, repeatedly.