Tidal Wave is a documented cross between B+ and Penis Envy, which places it at the junction of the two most worked lines in Psilocybe cubensis. That parentage is why it shows up in so many onward crosses: it carries useful characters from both sides.
The TW4 designation refers to a specific numbered isolate taken out of the original cross rather than the cross as a whole. If a listing says TidalWave 4, that is what it means, and it is a narrower thing than a generic Tidal Wave syringe.
Numbered isolates like TW4 come from selecting a single stable phenotype out of a cross and propagating that alone. The number is the breeder's own designation for which selection it was.
Because those numbers are breeder-specific rather than standardised, we credit the breeder on every listing. A TW4 released by one breeder is not automatically the same selection as another's.