I am not exactly clear on what factors qualify something as tashmishei kedusha, so I am not speaking with any authority, but I can personally hear a qualitative difference between tzitzis, which is an actual chefetz of a mitzvah (ie: the Torah says “make tzitzis”) and a hair covering which facilitates a mitzvah (covering an ervah), but is not in and of itself a chefetz of mitzvah. To illustrate the difference, consider that there are various other ways of covering your ervah, (ex: you can shave your head or you can stay indoors and out of sight of men who are not your husband). On the other hand, the only way to be yotzei tzitzis is by wearing tzitzis. Again, I’m not an authority on the matter. Perhaps someone else can bring sources, proofs, or counter-proofs?
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