Defining EMF

Trying to help some students understand EMF and I think they are confused by what the text -book that they are using stated:
"If a conductor, such as a copper wire, crosses the lines of force, the outer electrons in the atoms in the wire are freed and begin to move from atom to atom. This movement of the electrons results in an excess of electrons on one end of the conductor and a deficiency of electrons on the other.  This difference in charge is what we will later describe as voltage, or electrical potential.  It is this electrical potential that causes electric current to flow."

• This is confusing and leads the reader to believe that electrons move before an EMF is produced.
• a better description posted on Wikipedia: "An emf is induced in a coil or conductor whenever there is change in the flux linkages"  This is a better description as it tells the reader that the change in flux produces an EMF that has the ability to cause current to flow in the wire.

Is the first definition bogus ?  or does it follow what the current understanding of EMF ?

Thanks