Electronic – Electrical Consumption of Machine

Maxim has an app note showing how to use their high-side current sensor parts. They also show a basic op-amp circuit as the "traditional" way to do this measurement, and this is probably good enough for your application:

The output from this circuit could be run to a comparator to generate a digital '1' whenever the pulse is "on" and a '0' when the pulse is off. Some low-pass filtering may be required between the sensor circuit and the comparator if there is bounce or noise during the on and off transitions of the current pulse.

Then you have some choices.

In a simple digital logic solution, using probably a fairly modest CPLD, the digital pulse could clock a counter. The size (number of bits) of the counter depends on the maximum frequency you want to measure. A clock circuit would be needed to generate a pulse every 7.5 seconds. The 7.5-second pulse would be used to latch the counter output into a second register, while simultaneously resetting the counter. Some additional refinement would be desirable to avoid latching the counter output while it is the middle of rippling up the result of a newly arrived pulse from the comparator. The latched register, multiplied by 8 (left shifted by 3) would give the pulses-per-minute in the previous 7.5 second interval.

The digital pulse could be input to a microcontroller to count pulses and output how many pulses were seen in the past 7.5 seconds (multiplied by 8 to get pulses per minute). Or, count how many seconds are needed before you receive maybe 10 pulses from the comparator. The micro is more flexible than the CPLD in terms of letting you vary the counting interval depending on the actual frequency, averaging over multiple periods to get a smoother display, being able to change the units of the display, etc., etc.

How you display the output is up to you.

The issue you're confused about seems to be the difference between power and energy.

Energy is how much work you can do. Common units are joules or watt-hours.

Power is how fast you do work. It's a rate of change. Common units are watts or horsepower. Horsepower is probably an instructive unit to consider. Say you wanted to move a large pile of straw. Whether it's moved by a horse or a housecat doesn't affect the amount of work done. But the horse does it faster, because it's a more powerful animal.

For the purposes of discussing grid electricity consumption, watts (W) and kilowatt-hours (kWh) are the most common units used. To know how much energy is consumed, multiply the power by the time. 100 W x 1 hour is 100 watt-hours, or .1 kWh. In short, the relationship between power and consumption is time.

A 100W bulb consumes 100W assuming the voltage across it is what's specified on the package, which is usually 120V in my experience. If the voltage at your socket is lower, the bulb will consume less power. It's approximately a fixed resistance, so the power consumed is $$ P=\frac{V^2}{R} $$

As an aside, remember energy conservation. If something consumes 100W, that energy is being converted to some other form. Either it gets stored (potential energy), it's used (light, motion, etc.), or it's wasted as heat. For an incandescent bulb, ~90% of the power consumed is converted to heat. So a 100W incandescent bulb consumes 100W, but only outputs 10W of light. It gets hot because the other 90W is being wasted. Which is why CFL's run so much cooler and consume less power for the same light output.