H.264 in context of MPEG is MPEG-4 Part 10 "Advanced Video Coding", published in 2003. It's probably what OP is referring to, since pretty much no one on the web uses the other MPEG-4 video coding (anymore), MPEG-4 Part 2, which dates to 1999.

MPEG-4 Part 2 was made famous by the encoders DivX and Xvid, but didn't see the magnitude of professional usage as either its predecessors MPEG-2 Part 2 (also known as H.262) and H.263 (which was a teleconferencing codec to which the widely-deployed Sorenson Spark, used in Flash 6 and 7, was fairly close to) or its successor H.264.

That being said, the MPEG LA maintains a (very, very long) list of patents [1] in the H.264 patent pool, with recently expiring patents (sometimes?) notated for convenience. Submarine and unlisted/uncovered patents notwithstanding, an interested party should be able to start with this list and research if they are truly necessary to implement decoding and encoding of H.264 as used on the web today.

[1] http://www.mpegla.com/main/programs/AVC/Pages/PatentList.asp...

H.264 is a subset of MPEG-4. It's another name for MPEG-4 Part 10 (Advanced Video Coding).

MPEG-4 itself includes many other parts, including a container format, audio (AAC), and another video codec (Part 2, popularly known as DivX).

H.264 is MPEG-4 Part 10. If I am not mistaken H.264 is only the video compression part, while MPEG-4 is full audio, video, and container.

No, H.264 is a newer codec.

Now the fight is H.265 vs AV1.