There is a radio station in NYC, CD 101.9, that bills it self as a broadcaster of "cool jazz". Most of the cute pop-jazz that they play is not jazz at all.
During the forties and fifties, as Kublakhan points out in his inimitable style, a "cool school" of jazz playing was thriving along with the bop and hard bop of that time. This cool approach to jazz playing was characterized by a more laid back attitude, quieter energy, and softer and warmer tone qualities with less edge in the sound than was common in the hard bop style. Sometimes, European forms such as the rondo (Brubeck's "Blue Rondo A La Turk")were used. Notable exponents of this style were: Dave Brubeck, Chet Baker, Paul Desmond, Gerry Mulligan, MJQ, and of course Miles, whose "Birth Of The Cool" sessions get my vote for "best". "Kind OF Blue" really doesn't belong to that style; it is more indicative of the burgeoning "modal" movement in improvised jazz. Regards.