they're both two different things. they won't have any duplicate flourishes, but in Trilogy, you can see some flourishes which have actually (i guess you can say) "evolved" from the ones taught in the System.
you also have to remember that the Trilogy not only teaches you flourishes, but also magic routines and miscellaneous items that the twins have come up with or have had permission to teach. the trilogy also has a section called "Flourishing 101" which briefly goes over some basic flourishes like the Sybil, one handed revolution, Lee Asher's "ripper", etc.
hope that helps.