Very basic question I assume, I'm a maths student with a physics background. I remember magnetism to be defined as the phenomenon induced by a magnetic field. I remember that the force exerted by a magnetic field on an electrically charged body (most probably a point charge) was given by $F=qBv|\sin(\vec{B},\vec{v})|$ in scalar terms. But when you stick a magnet onto a fridge, there need not be initial velocity for this to work. And I also feel that there need not be any electrical charge involved, but I can't say that for sure since the magnet is made of atoms.
So are those different types of magnetism ? I would like to think they are related and that the fridge magnet is just a macroscopic response to the formula.