For the sake of those with little or no technical knowledge, let me try to explain a few concepts.
VOLTAGE (symbol V or E) - Voltage is the presents of Electricity. Think of a battery sitting on a shelf. It still has voltage even though it isn't connected to anything. The Voltage is present it is just not being used. Think of a water tower full of water, but all the taps are turned off.
CURRENT (symbol I) - Current is the movement of Electricity. Connect a battery (a voltage source) to a Bulb and current flows, draining the battery and lighting the bulb. When current flows, work is done. So, Current is the Flow of Electricity through wire.
RESISTANCE (symbol R or the Greek letter Omega) - Think of this as a restriction in a water pipe slowing the flow of water; as in Low-Flow Shower Heads. The Water Tower represents Voltage, it has a certain amount of water pressure which equates to voltage. But regardless of the pressure in the water lines, the Low Flow Shower Head resists, restricts or limits the rate of flow of the water.
In a sense, we can think of a Resistor as a device that controls the flow of current in a circuit. Big resistance means small amounts of current. Low Resistance means large amounts of current.
IMPEDANCE ( symbol R, Xl, Xc) - This gets complicated. If we are dealing with pure Resistance, then Resistance and Impedance are the same thing. However, if we are dealing with Capacitor or Coils, it becomes more complicated. The nice thing about a Pure Resistor is the the Current and Voltage are in sync. As soon as we have Voltage, we have current and the math is very easy - Add, Subtract, Multiply, Divide.
But, that is not true of Capacitors or Inductors. A Capacitor is like a big bucket, water flowing into it is like current flowing into a Capacitor. The level of water in the bucket is analogous to Voltage, the more water in the bucket, the higher the voltage.
But look what is happening from the perspective of the Bucket or Capacitor. Current Flows fast and immediately, but it take a while to fill the bucket. So, FIRST come current, then comes voltage. The Current and Voltage are out of sync with each other. Which means we have to use VECTOR Math to solve any equations using Capacitors (or coils).
With Capacitors the Flow of Current LEADS the presence of Voltage by 90°.
Let me say here, that this only applies to alternating or changing voltages. Capacitors and Coils are unaffected by DC or continuous voltages. To a DC voltage, a capacitor is an open circuit. To a DC voltage, a coil of wire is a short circuit.
The opposite occurs with a Coil of wire. Because a coil of wire is also a generator. When Voltage is applied, the coil creates a counter Voltage that resists the flow of current. As the CHANGE in voltage subsides, that is, as we get closer to a DC Voltage this counter-Voltage disappears and current begins to flow.
So, first we have Voltage, then we have Current. So, the Voltage LEADS the Current by 90°.
This is why speaker design is so complex. If speaker were purely resistive, it would be simple. But speaker are a complex combination of Capacitance, Inductance (coils), and Resistance. As a result, as the frequency varies, the impedance of the speaker is all over the place. At one point, the Resonance Frequency where all the factors (capacitance, inductance, and resistance) are at their peak, an 8 ohm speaker can be as high as 80 ohms. On either side of this peak, the impedance is at its lowest, and an 8 ohm rated speaker might drop down into the 4 ohms to 6 ohm range. Though 6 ohms is more likely. Then are the frequency starts to rise, the impedance also starts to rise, and at the very highest frequencies, the impedance can be back up around 60 ohms.
As you can see IMPEDANCE is a very complicated thing, and drives speaker designers Barmy.
POWER (symbol P or W) - Power is the result of something, not the presents of something. Voltage is the presence of Electricity. Current is the presence of the flow of Electricity. Power is the result of a Voltage being applied to a Resistance/Impedance causing current to flow, resulting in Power being consumed or work being done.
We assume that amps provide Power, but not really, they provide voltage, and as a result Power is consumed by the speaker. An amps Rated Power is the measure of the Voltage and Current capability of the amp. The more Voltage it has and the more Current it can supply, the more power the speaker is able to consume.
With more Voltage and with higher Current, the brighter the bulb lights.
In the specific case being talked about, using an 8 ohms speaker in place of a 4 ohms speaker, is not likely to cause any problems. However, going the other way, using a 4 ohms speaker in place of an 8 ohm speaker COULD cause a problem, depending on the quality of the amp.
Other factors come into play, one factor is time, another factor is Volume or Loudness.
I used an 8 ohms speaker and a 6 ohm speaker on a normal consumer amp. Technically this shouldn't be allowed since the combination of those two speakers is 3.4 ohms. Typically 4 ohms is the low limit on a vast majority of amps. On two different consumer grade amps, this worked. That is until I used the system to watch a movie (Lord of the Rings). Part way through the movie, the amp shut down; too much volume for too long a time.
Again, if my facts are right, in the current discussion, it is very unlikely that using an 8 ohms speaker in place of a 4 ohms speaker would cause a problem. The current will be lower and the heat will be lower; I don't see how that could cause a problem.
Just a few, hopefully helpful thoughts, though long winded as usual.
Steve/bluewizard