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.