H.263 was a sole development of the ITU but I wouldn't bother all too much with the specified use case of video conferencing. It's a codec with the main purpose of improving the compression compared to older codecs which of course is beneficial for video conferencing where bandwidth is a very limiting factor, especially at the time the codec got developed.
The MPEG then developed MPEG4-Part 2 which is based upon H.263 and offers bit-stream compatibility to the base-line level of h.263, meaning there is a h.263 compatible bit-stream in an MPEG4-Part 2 encoded video that you could call the basis for the actual MPEG4-Part 2 video stream that extended the h.263 compatible stream. So MPEG4-Part 2 offers a few more features than h.263 but essentially they are very closely related.
With MPEG4-Part 2 started this weird age of many companies making their own implementation of these two codecs resulting in a few new container formats that were only used by these specific implementations f.e. RealMedia's .rmf/.rmvb or DivX's altered version of AVI, .divx.
RealMedia even made their own codec again based on h.263. A horrible age of a ton of different formats that needed their own browser plugins and players because they weren't fully compatible to each other, either because of their container or slight alterations to either h263 or MPEG-4 Part 2.
Which made this codec generation a bit special, while .MP4 was already present at the time in an early form it was barley used as the container format for MPEG4-Part 2. So h.263 and MPEG-4 Part 2 was found in a ton of different container formats unlike h.264 which has is also found in several container formats but with the intended container format MP4 being the defacto standard that is found everywhere. The most popular alternative being the open source Matroska container format (.mkv/.mka). Apple's QuickTime .mov also supports h.264 but even in the Apple Ecosystem MP4 is dominating. In my opinion the biggest reason why h.264 is such a huge success today.
DivX began as a reversed engineered version of Microsoft's MPEG4-Part 2 implementation. At that point there was no company behind DivX, it gained popularity because of its good compression at that time and also being free to use.
After DivX made it into a company they revamped the code for the codec as it was still based on some Microsoft code.
Though it still was an MPEG4-Part 2 implementation after the rewrite and became a pretty popular codec that was supported by a lot of DVD players at the time. Some developers of DivX went on and made the open source version called Xivd (that used AVI instead of .divx) that gained a lot of popularity in the movie "pirating" scene and was their standard for encoding videos for several years until h.264 came along. Though even after h.264 was readily in use by consumers Xvid was still used for a few years because of it's good understanding in the scene. It became somewhat of an art to encode movies in Xvid because of all those sophisticated encoding options available in the Xvid encoder.
Xvid had a few advanced features that weren't implemented in DivX which made videos encoded with those feature in-compatible with DivX certified devices.
Since MPEG4-Part 2 the MPEG and ITU-T are jointly developing codecs, H.264 being their first co-operation. This is the reason why the codec is often referred to as h.264/MPEG4-4 AVC. MPEG-4 AVC being the MPEG's/ISO name for the standard and h.264 that of the ITU-T. Different names but identical standards. The same goes for h.265/HEVC.
I hope that helped a bit clearing things up, though a lot of this is also knowledge taken from Wikipedia, so it might not be new to you but I tried to put it an order that made sense.
