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"
