Acme or Apex?

When I was a child, I lived next door to a neighbourhood corner store called Apex Grocery. When I asked what apex meant, my father told me that it meant the top of a hill. And, in fact, our house and the store were at the top of a hill. Curiosity satisfied. For the moment.  
 
Over the years, I kept hearing the words apex and acme used almost interchangeably to mean the top of something. I wondered why we would need two words to mean the same thing. Do they mean the same thing?
 
The word acme appears in English in the 1560s from Greek akme (the highest point, the peak of anything) and Proto-Indo-European (PIE) ak-ma (to be sharp, to rise to a point).
 
The word apex appears in English around 1600 from Latin apex (summit, peak, tip, top, extreme end) and PIE ap-(1) (to take, to reach).
 
Given their similarities, how are they different? In brief, apex usually means the actual top of something; e.g., the apex of hill or mountain or trajectory, the top of a pyramid. In nature, an apex predator is an animal at the ‘top’ of the food chain.
 
On the other hand, acme tends to be used more subjectively; e.g., this hotel suite is the acme (the height) of luxury and comfort or she is the acme (an exemplar) of good taste.
 
Curiosity satisfied. Again.
 
Reference: Online Etymological Dictionary, https://www.etymonline.com/