Terminology-wise, how do I differentiate between a "percentage percentage" gain, and a "additive percentage" gain? Sorry if the question title is confusing - I'll explain.
I often have to provide answers like "If we did X, than Y would be P% larger."  This is fine if the units of Y are "absolute units."  For example - "If the plant is given food twice a week instead of once, its expected height after 3 months is 12% higher."
However, I never know how to phrase it when the units of Y are already percentages.  For example, say I'm measuring how many people click on an ad.  Assume that currently, 30% of people click, but if we change the ad's wording, 42% of people click.
I could say that that is a 40% increase in click rate (because 42/30 = 1.4; this is my "percentage percentage" gain).  Or, I could say that it's a 12% increase in click rate (because 42% - 30% = 12%; this is my "additive percentage" gain).
At times, I'll want to give both values, but obviously this gets very confusing.  Is there correct terminology?  Concretely:

*

*If I wanted to say that changing the ad wording causes a 12% increase, from X% to (X+12)%, how should I say that?


*If I wanted to say that changing the ad wording causes a 40% increase, from X% to (1.4 * X)%, how should I say that?
Thank you!

I think you are describing Percentages (2) and Percentage points (1).
More details here.
