No. I guess they could both be considered progressive rock, but the bands are quite different and are not related to each other.
Crimson King was created in 1994.
radiohead, king crimson, massive attack also the Peaches and the Yeah Yeah Yeahs
at an ASIA show
The Compact King Crimson was created in 1986.
King Crimson on Broadway was created in 1995-11.
Heartbeat - King Crimson song - was created in 1982.
People - King Crimson song - was created in 1995.
The Court of the Crimson King was created on 1969-10-12.
Touched by the Crimson King was created on 2005-06-27.
Exiles - King Crimson song - was created in 1973.
Islands - King Crimson album - was created in 1971-12.
Red - King Crimson album - was created on -19-08-07.