Most attractor patterns resemble little in the forms of a hatch. They tend to work off of a hotspot of color or a particular movement or flash of material. A Royal Coachman, Turks, Patriot, bright humpies....etc. Many of them may have a down or upwing profile....but most flies do in general.

Most of what is referred to as a "search" pattern tends to be a fly that resembles a hatch on a particular water. Something that while not matching a current or non-existent hatch, is familiar to the fish and is a logical "guess" as to what may pound up fish. A Caddis, Stone, Haystack, Adams, Bivisibles or even a Wulff tied to match a local hatch in size and color.

Is it an approach?....yeah. More so than a tying style. And an attractor pattern can double as a search pattern. But generally the reverse wouldn't be thought in the same way.

I would say it is a little grey at best. I would not identify any one person as being the "defining" opinion...because there really is no exact answer.

One more thing. Look in tying manuals. There is almost always an "attractor" category. Which has nothing to do with how it is applied on the water.