The big question in the different types or grades of tzitzit is lishmah, i.e. with intention. According to halacha, when making tzitzit you must have the mitzvah of tzitzit in mind. You cannot simply buy or make strings and then call them tzitzit.
The question, then, is from what stage of the tzitzit making process is intention required?
How are tzitzit made? The main stages in the tzitzit production process are known as gozez (shearing), libun (bleaching), niputz (carding), tevia (spinning) and shezira (plying). The basic halacha requirement stated in the Shulchan Aruch (O.C. 11:1) is that you must have tevia lishma (spinning with intention). The Rema notes that according to some opinions you should have niputz lishmah (carding with intention), though he adds that the custom is to be lenient.
Occasionally you will find tzitzit strings known as “lashonot tzemer,” which means they were made with intention starting a bit before the tevia (spinning). In English, “lashonot hatzemer” is wool rovings, which are pieces of wool that have been combed, drawn into a clump and then twisted slightly to hold the fibers together and to prepare them for spinning.
The Mishna Berura explains that the mitzvah of making tzitzit (ta’aseh lecha gedilim) starts with tevia, however, he notes that the Prisha states in the name of the Maharal of Prague that one should try to obtain tzitzit with niputz lishma. The Aruch HaShulchan concurs with the Maharal of Prague.