From what I've been investigating, the big difference is that the beach wavesare wider and the curl is not as perfect. In mermaidwaves, the curls are more delineated and bigger, a little bit like Shakira hair style you know what I mean?
Also the beach curl works better with spray and the mermaid with mousse.
In my opinion, no matter the name, there is nothing better than having the most natural and healthy hair. So keep in mind to use good products that protect the hair from all the mess we normally do with it.