Difference between caps for coupling or crossover

I'm looking for good quality output coupling caps to modify my OPPO player. There are endless dicussions and listening tests everywhere, but one thing is still unclear to me. Is there a difference in the type of cap you need for crossover applications and (signal) coupling? Most online tests, like the famous 'Humble homemade hifi' pages, use the caps in crossovers. Would the results transfer to coupling applications, or are the two different?

In general, what would be the requirements for the perfect coupling cap? And how would they be different to the requirements for crossover caps?