I never said it was a codec. It is a file format that offers better compression. That's why a 1920 x 1080 video in an .mkv container is smaller that the same video in .mp4 format
That's simply not true. MP4 and MKV are containers with low overload, unlike MPEG-2 TS where the container overhead can add up to 8-10%, especially for low bitrate audio and video.
Containers have nothing to with how much video is compressed. While MKV can have compressed headers, this makes little difference unless you're dealing with video that is either low resolution or was compressed so much that it has a very poor quality. MP4 does not have 700MB of overhead compared with MKV, and if you're finding that the file sizes are that different, it means the video has been compressed significantly more in the MKV by the video encoder, not the muxer (multiplexer). Or maybe one has used a different codec, such AV1 vs. AVC. Demux your streams and then see what the size of the elemental video streams are if you want proof.
Yes, I work at a codec company. And no, I haven't seen MKV for years, it's a format popular with certain online communities like the DivX crowd or pirates (often the same people).