Ferrites that are used in transformer or electromagnetic cores contain nickel, zinc or Manganese compounds. They have a low coercivity, and are called soft ferrites. Because of their comparatively low losses at high frequencies, they are extensively used in the cores of Switched-Mode Power Supply (SMPS) and RF transformers and inductors.
In contrast, permanent ferrite magnets (or hard ferrites) have a high remanence after magnetization, and are made with iron oxide and barium and strontium oxides. In a magnetically saturated state they conduct magnetic flux very well and have a high magnetic permeability. This enables these so-called ceramic magnets to store stronger magnetic fields than iron.