Both Miles and Coltrane were moving away from the dominant jazz style of the late 1950's (known as hard-bop), but in different directions. For example, whereas Miles implemented more static harmonies and a relaxed tempo in his classic So What, Coltrane did the exact opposite in the landmark Giant Steps, filling the tune with many then unfamiliar chord changes and taking it at a blistering pace.
Miles Davis's Kind of Blue had come out a couple of months earlier, just a few months after John Coltrane's Giant Steps, each disdaining chord changes in favor of solemn inquiries into chords and modes. Davis's So What coolly navigated between a couple of minor Mixolydian modes; Coltrane's Giant Steps circled the circle of fifths.
Go read Stefan's post to see what is embarassingly wrong about Yaffe's descriptions. But more importantly, this wrongness is compounded by the inscrutable jargon that tries to keep the audience from seeing the author's lack of knowledge. (See Calvin the academic)
The newspapers that have been canning their music critics don't understand the need for this specialized knowledge. Your average graduate of journalism school will not know the differences between Schoenberg and Stravinsky, much less between Augusta Read Thomas and Joan Tower. I also acknowledge that your average graduate of a music conservatory cannot express him/herself in writing well enough to get across these differences*, which is why a good music critic is so valuable. Write your local editor to either praise the local music critic or demand a good one. Even if newspapers are transforming into a different form of media, they still are the record of all important local events.
*I've been trying to change that with my seminars on music writing, though I'm not teaching it this coming year.