Do I need to set different formats for mobiles and Web?

Depends on the protocol you use.
The video industry and mobile landscape changes all the time.
For HLS, MPEG-DASH and RTMP streaming, it is recommended to have a fallback with a MP4 - H264 video codec and AAC audio codec to play it on most browsers and mobile devices.
With version 8, it is even possible to set 2 fallback options.  The player is intelligent enough to serve the correct protocol supported by the device in use.

In version 7 and lower, it is possible to set a low resolution video as HTML5 fallback if you use private RTMP streaming. It needs to have the same name as the HD version, but it can reside in another bucket.

Updated: December 18, 2017