what are two examples of tasks for which each kind of magnet would be suitable?

Answer 1

It would be helpful if you mentioned what kinds of magnet your out-of-context pasted question was about. Electro vs permanent? AC vs DC? Bar vs horseshoe? I'll assume electro vs permanent.
A typical electromagnet example is the large type used in junkyards to separate iron-based metals from others. This magnet is lowered by a crane onto a pile of mixed metal scraps and then turned on. It picks up the iron-based scraps and then is moved over a dump truck, where it is turned off so it drops the scraps into the truck. The ability to pick up and drop on a simple command (turning on/off) makes such magnets very valuable tools.
A permanent magnet is useful anywhere a steady magnetic field is desired. Refrigerator magnets and field magnets for small motors are examples. These magnets save electric energy that would be needed if an electromagnet were used.