Good coaches aren't labeled. They coach to their teams talent. That's what made Johnson so good in Philly.
I assume you mean Johnson in Dallas, so I will address it that way.
Jimmy was a defensive guru. That's not a label. His "upfield pressure" model revolutionized defense. "Read and react" is gone today, and most every team whether it be a 3-4 or a 4-3, whether it be college and even high school, runs the upfield pressure scheme today. As far as offenses go, he couldn't have cared less about it. Defense was his passion.
For his upfield pressure scheme he needed a certain type of defensive lineman to run that scheme and he chose them accordingly, starting with the Selmon brothers. And in Dallas he did the same thing. Brought in the talent he needed to run his scheme. NOT merely coaching to the talent that was there.
On the offense, he brought in people to run their schemes and didn't interfere. THOSE people, notably Norv Turner, coached to the strengths of the offensive talent.
You said good coaches aren't labeled. No, good coaches label themselves with their core beliefs and philosophies they hone over decades.