In an ideal world all BSP threads would be taper. That way, as the fitting is inserted, the thread tightens and seals. With a parallel thread, there will always be a degree of play, making it difficult to seal. A parallel thread would be used if it was intended to accept something like a union nut. Having said that, most copper x iron female fittings tend to be parallel anyway.
Put it another way. If iron pipe was being used, all threads cut on the pipe would be taper, as would the fittings. An example of a parallel thread would be the stem of a bath tap, where a nut is run up to secure the tap, and a union type fitting is used to connect to the pipe.
I found that rather difficult to explain, not easy without a demo, and I bet I've confused you even more !
If you have any more problems, it would be best to post a photo or two, so we can see what's going on.
. Hope the project went well