If I filter the data on Analytics per channel, I see much fewer/no plays, while if I search for the same channel in VideoManager Pro, I can see that the connected videos have much more plays.
The tracking of videos filtered by channel works based on the information in the embedded code. The channel ID information is normally contained in the standard proposed embedded code in the publish accordion in VideoManager Pro. In some cases (e.g. the video does not belong to any channel) there would be no channel attribute in the suggested HTML-embedded code; or if the video belongs to more than one channel, in the suggested HTML code there is the attribute of one channel rather than the channel from which you wish to track data. Moreover, the code you see here in VideoManager Pro is only a suggestion, it may be that your IT-Department embedded the videos with a different embedded code (which may not include the channel ID attribute).
Embedded code with channel attribute:
<div mi24-video-player video-id="3UJsjxDi-oqCTKnrTP7px5" player-id="FRYbAzxBZoABXc1X4U122J" channel-id="97874" config-type="vmpro" flash-path="//e.video-cdn.net/v2/" api-url="//d.video-cdn.net/play"></div><script src="//e.video-cdn.net/v2/embed.js"></script>
Please, note that such channel attribute has no functional purposes (the video in the playout works perfectly fine without it) and is only intended for tracking purposes.
So, in case the plays filtered per channel in Analytics (when the time range selected is correctly set up) are much fewer than the sum of plays of all videos that are connected to one channel in VideoManager Pro in the same time range, this might be due to the way videos are embedded. You would need to check if the channel ID attribute is in the embedded code.
You can find the channel ID of the respective channel, by selecting the channel, in the browser URL.