They are certainly both 20% more efficient and 20% more powerful. Let's say that a certain size panel gets 100W of insolation. If you move from 20W to 24W then you are generating 20% more power from the same amount of insolation, so you are 20% more efficient.

People seem to treat percentages differently from other numbers, when all it means is "divide by 100." Nobody complains when you say going from 9% to 18% is "doubling in efficiency" but if you say it is "100% more efficient" or "200% as efficient" then people complain.

If you were going to buy these, you'd find you need 20% fewer panels (of the same area) to generate the same amount of power.

Sounds like the marketing team is right about this one.

4 / 20 = 0.2 aka 20 percent.

Your 4% are not percent, but percentage points. The marketing team is right about this one.

I'm afraid you are wrong, what you are referring to are percentage points [1].

[1] https://en.wikipedia.org/wiki/Percentage_point