MOV vs 3gp vs MP4 File Format

well it's the formats for different camera types,
different compression of the video frames so that the designated programs can use them. Higher quality.
 like in long play on a vcr  to short play more pixles are squashed into a frame,,
like FM and AM use different frequencies.
It's all about the battle of ownership really to make money and to bring that extra video quality.
Microsoft owns WMV.
mpeg1/2 /mpg is owned by the motion picture experts group so no microsoft software will run mpeg without codecs. That's DVD/ VCD

3gp is small high definition for mobile phones.
3GP is a multimedia container format defined by the Third Generation Partnership Project (3GPP) for use on 3G mobile phones.
http://en.wikipedia.org/wiki/3GP

Mov has the largest frame rates of these three and is owned by quicktime
http://en.wikipedia.org/wiki/MOV
MP4 is also high definition but for ipods--owned by QT mpeg4 is the alternative name for this codec.
http://filext.com/file-extension/MOV
http://en.wikipedia.org/wiki/QuickTime

So the advance in video is the new 3gp high definition  since all video regardless needed to be converted to mpeg2 for DVD.
mpeg owns the monopoly of  video codec for DVD in the world until now
Blueray.
http://www.blu-ray.com/info/
Origins of the Blu-ray vs HD-DVD War
http://www.roughlydrafted.com/2007/08/29/origins-of-the-blu-ray-vs-hd-dvd-war/

Hope this helps you

Thanks, but it does not really answer my question, Please let me explain what I mean:
(1) I am interested in the following 3 video codecs:
MPEG-4 Part 2 or H.263 or MPEG-4 Part 10 (AVC/H.264)
and in some standard audio codecs - AMR, AAC etc.
(2) All the 3 containers I was asking about (mov, 3gp and mp4) support these codecs!
(3) However - each container (mov, 3gp and mp4) implements a new transport stream (aka file format, for example ISO/IEC 14496-14 that supports any codec!) a transport stream is just a multiplex of audio and video decoded (no matter what codec) streams, and other data, for example subtitles streams (usually in subtitles standard, for example SSA or ASS, but again - it's not important for the container itself!)

so my question is if somebody can highlight all or some of the differences between the transport streams?

I don't have those answers for you if it even has an answer transport streamsare defined on the software and transport of the product used.
Maybe MerijnB will come back now :)

SCSI Standards Architecture
http://www.t10.org/scsi-3.htm
I'll have to refer you to the famous Wilki sorry
MPEG transport stream
http://en.wikipedia.org/wiki/MPEG_transport_stream
Transport Stream Analyzer for HDTV standard
http://www.codeproject.com/KB/cs/transport_stream_analyzer.aspx

Thanks, but I am still not closer for finding a solution for my problem. Please let me explain my problem in details, maybe somebody here is an expert and would be able to answer:

MP4 and MOV file containers should be very similar. MP4 is based on MOV. As far as I can understand the documentation, MOV supports all the MP4 atoms types plus some more:
http://www.mp4ra.org/atoms.html

However - when I rename an mp4 file to mov, QT cannot open it. Why?