Refer the basic conduction mechanism in electric circuits. It is based on the surface charge feedback mechanism of electrons. In a dc circuit,when we say there is a voltage drop across the resistor, there is actually surface charge gradient along the resistor which is responsible for creating the necessary electric field inside the resistor. Due to this charge gradient,voltage is present.Voltmeter senses this charge gradient and current is established in the voltmeter.This current is proportional to the charge gradient and hence, to the voltage across the resistor.Voltmeter reads the voltage due to surface charge gradient only.Thus,voltmeter only reads static electric fields.
For a conducting wire,the gradient of surface charge is so small that voltmeter draws almost negligible current,hence shows 0 voltage.That doesn't mean entire wire is at the same potential. Only for convenience,we assume so.
Now,in case of induced fields, there is no question of charges. They just APPEAR whenever there is a change in magnetic flux(It is governed by a beautiful part of physics,called Maxwell's equations). So voltmeter can't read any induced field.**However,if you break the loop and attach voltmeter in the gap,it sure will read the voltage. Because,**the induced field will cause the electrons to move opposite to the field so as to cancel it and they will accumulate at one end and start forming a gradient. This process will stop once the field due to gradient exactly equals(or cancels,precisely) the induced field. So,now we have voltage due to a static electric field which is equal to the induced emf. Thus,voltmeter reads it. This also explains why E-field inside a conductor placed in external field is 0,as stated by Gauss' theorem.
(In a DC circuit,this Guass' statement isn't true as there is a field inside the wire. Is Gauss wrong?? Try this question..Its really interesting!!)
The process of formation of these electron gradients is transient in nature.It is called surface charge feedback mechanism.It occurs due to natural initial imbalance between fields and charges.It takes a few pico-seconds to complete.It is really the 'common sense' of circuit theory.
Visit youtube for video lectures on this mechanism. Hope this helps...Good luck!