Big difference in the video file size after the conversion (.mov to .mp4)
Let me explain you from scratch.

MOV, MP4, AVI, MKV etc all these are just containers, It is just kind of wrapper which contains audio, video, text, metadata file together as one file. It does not play a big role in the size of a file. 

Size of the file heavily depends on audio and video codec and bit-rate of that audio video codecs.

So there is a possibility for file size reduction during conversion.


Reduce in video codec bitrate. While converting video if default/changed bitrate of video codec is less than source file, then it will lead to a reduction in file size as well as quality for sure.[ May not be perceivable by eye ] 
Change video codec. While converting video if change video codec to advance video codec of the stream, then it will reduce size but quality will not be degraded.


For example : 
Video codec of a source file is MPEG-2 with bit-rate 20mbps and during conversation we convert to H264/AVC with bitrate 10mbps it will have the same quality with half of the size. 

So, Below are the popular video codecs generation and improvement.

MPEG-2 -> H264 (40-50% bitrate reduction than MPEG-2) -> H265/HEVC (40-50% bitrate reduction than H264) 

Though the more advanced codecs are computationally expensive during video playback. e.g H265 is ~300% more computationally expensive than H264.

During video conversation point 1. &amp; 2. both can be applied 

You can view details of audio/video file can be seen using a free tool (mediainfo)
It will show properties of the stream like video codec, bitrate, fps etc.