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Voltage drop across a component describes the reduction of energy when current moves through passive elements, is this the same as voltage across?

What about for capacitors, technically current does not actually travel through the dielectric, can this term still be used for capacitors?

Voltage drop across a component describes the reduction of energy when
current moves through passive elements, is this the same as voltage
across?

Voltage drop and Voltage across the component mean the same thing, assuming the same component and the voltage across that component.

What about for capacitors, technically current does not actually
travel through the dielectric, can this term still be used for
capacitors?

You can measure voltage across capacitors, which is dependent on the time value of the current.

Yes, they're the same, although I think that most people would want to reserve the phrase "voltage drop" for the voltage developed by running current through a dissipative element such as a resistor, relay, or diode junction.

As a counter-example, referring to a "-9V drop across the battery" would be somewhere between odd and positively strange.

Along with the other fine answers, I would add that one term may be more suitable than the other, depending on how it is used.

For example, I was recently teaching some basics to a beginner and the conversation included statements such as:

“Due to the voltage drop of R1, the voltage at point A is now...”

and,

“What is the voltage across R1?”...

In the first case, I used “voltage drop” to help keep focus on the fact that our reference for the calculation we’re interested in (i.e. the voltage at point A) is still ground.

And I used the other to imply that the reference is just beyond the element R1.