Which tools are most likely used to create animated video (i.e. corporate commercials)?
I can't be really sure, but most of that can be done using After Effects and a simple screen recording. You record the screen of a phone, put that into after effects, get a picture of a hand and put that into after effects, and just move it around with the frames.

The whole of screen recording could also be made using Adobe Flash or After Effects instead of actually taking it, but it would take a while... This way you could create a minimal and simple version of your app or something, which might be more eye-pleasing and less complicated to the audience.