Inductors store energy. Transformers, well, transform power, storing a minimum of energy.
Energy is stored in air gap. In fact, the energy density goes as Bsat^2 / (2 mu).
It is advantageous, for a transformer, to use as high mu as possible. The high inductance causes low magnetizing current, and low energy storage. Ferrites for power conversion start at mu_r = 1k or so, going up to about 15k for pulse transformers and common mode chokes (which, despite the name, aren't for energy storage, so are actually transformers; which makes sense and should be the case, when you consider the meaning of "common mode").
It is advantageous, for an inductor, to use a modest mu. Too low and the voltage drop across the winding's resistance is too large, relative to the EMF developed (low Q and low efficiency). Too high and the magnetizing current is too low to store enough energy to be worthwhile. Somewhere between "air core" and "ungapped ferrite", there exists a rough maxima, where efficiency (Q factor) and energy density (physical size for a given L @ Ipk) are best.
Powdered iron essentially has a distributed air gap, being made of particles packed together and bonded with resin. (Whereas ferrite, and steel and amorphous metals, are solid with little or no internal air gap.) This leads to a modest (average or equivalent) mu, suitable for inductors.
What mu is optimal? Given the resistivity of copper, the range of frequencies needed in power conversion, and typical tradeoffs between efficiency and size, a mu_r from 10 to 75 is typical.
Ferrite is perfectly suitable, indeed almost always better performing, than powdered iron, as long as the core is gapped. This is rather impractical for toroids. Gapped ferrite cores are always shapes, usually designated as P (pot), PQ, RM, ER, E or C (or many variations upon them). The core set has two pieces, and a physical gap in the central limb (or in both the center and the outer limbs, in which case you add up both) provides the air gap necessary for energy storage.
Tim