The Flash player is for watching Flash videos (like YouTube) on the internet through a browser (like Safari).
The Perian component enables the Quicktime player is to watch Flash videos (like YouTube's Flash flv's) . Perian also enables the Quicktime to play a bunch of other codec/formats to be able to be played too. From the Perian web site:
Perian enables QuickTime application support for additional media:
File formats: AVI, DIVX, FLV, MKV, GVI, VP6, and VFW
Video types: MS-MPEG4 v1 & v2, DivX, 3ivx, H.264, Sorenson H.263, FLV/Sorenson Spark, FSV1, VP6, H263i, VP3, HuffYUV, FFVHuff, MPEG1 & MPEG2 Video, Fraps, Snow, NuppelVideo, Techsmith Screen Capture, DosBox Capture
Audio types: Windows Media Audio v1 & v2, Flash ADPCM, Xiph Vorbis (in Matroska), and MPEG Layer I & II Audio, True Audio, DTS Coherent Acoustics, Nellymoser ASAO
AVI support for: AAC, AC3 Audio, H.264, MPEG4, and VBR MP3
Subtitle support for SSA/*** and SRT
A good component to have...