Different result when using Motion Detection filter and converting, compared to "live" filter

[jimothyhalpert7]

I'm trying to save a video with motion detection rectangles.
However, when I convert the video with the enabled motion detection filter, I get way less rectangles, as compared to when I view the video, and the filter is enabled in the settings.
Windows machine. Video is .mov converted to MP4 with H.265, with keeping the bitrate, frame rate and aspect ratio same as in the original.
Am I right to assume that having these settings will not alter the video in any way, except adding the rectangles?
If so, then why is the result different, as compared to applying the filter "live"?

[Rémi Denis-Courmont]

The handling is quite different. Conversion does not need to be done in real-time, in particular.

[jimothyhalpert7]

Why would real-time affect the amount of motion that is recognize?
What we try to achieve the same effect in the saved version, as we see it in real-time?