What is the difference between H.264 video and MPEG-4 video?

They are names for the same standard from two different industries with different naming methods, the guys who make & sell movies and the guys who transfer the movies over the internet. Since 2003: "MPEG 4 Part 10" = "H.264" = "AVC". Before that the relationship was a little looser in that they are not equal but an "MPEG 4 Part 2" decoder can render a stream that's "H.263". The Next standard is "MPEG H Part 2" = "H.265" = "HEVC"

H.264 is a new standard for video compression which has more advanced compression methods than the basic MPEG-4 compression. One of the advantages of H.264 is the high compression rate. It is about 1.5 to 2 times more efficient than MPEG-4 encoding. This high compression rate makes it possible to record more information on the same hard disk.
The image quality is also better and playback is more fluent than with basic MPEG-4 compression. The most interesting feature however is the lower bit-rate required for network transmission.
So the 3 main advantages of H.264 over MPEG-4 compression are:
‐ Small file size for longer recording time and better network transmission.
‐ Fluent and better video quality for real time playback
‐ More efficient mobile surveillance application

H264 is now enshrined in MPEG4 as part 10 also known as AVC

Refer to: http://www.velleman.eu/downloads/3/h264_vs_mpeg4_en.pdf

Hope this helps.