Why are jet engine nacelles, used on the same plane, so different? One thing that is plainly obvious about the design and configuration of jet airliners is how little they tend to differ. 

It's surprising then that even on the same airliner, you will see two quite different-looking engines.

I've seen A330s with "fully-enclosed" engines, and "open" engines:

(Trent 700 with exhaust mixer, image from Wikipedia).

(PW4000 with unmixed exhaust, image from Wikipedia).

The fact that both designs are used suggests that one isn't simply better than the other, but the difference seems fairly significant. 

Why would an engine designer or a customer opt for one design over the other, and why do they arrive at such apparently different solutions for the same use-case? 

I assume, perhaps incorrectly, that each has its own advantages and that for whatever reasons different manufacturers and customers value different ones.
Sometimes manufacturers will certify with multiple engine types because their customers have their own power plant preferences (or manufacturer preferences, like say an airline's existing fleet is RR engines and they want to keep engine commonality for logistics benefits, or an airline feels one model engine is cheaper to run than another).  Providing different powerplant options for an airliner can therefore result in more sales.