Short Answer:
FLV is Flash 9, single-file h264 we know and love.
F4V is Flash 10, HTTP Dynamic Streaming (HDS) segmented streaming file similar to Apple HLS
Long Answer:
http://www.thekuroko.com/2011/06/articles/http-dynamic-streaming-getting-started/
HTTP Dynamic Streaming (HDS) allows for the delivery of streaming content over the HTTP protocol.
sample.f4m: This is an XML file created by the f4fpackager that contains the information necessary for a client player to playback the video file. There will be only one of these for each source video file.
sampleSeg1.f4f: This segment file contains the fragments that the client player will request for playback. There can be multiple of these files for each source video file.
sampleSeg1.f4x: This is an index file that contains specific information about the fragments inside the segment files. There will be one of these types of files for each segment file. The HTTP Origin Module uses the data in this file to determine the fragment to send back to the client after a request.
