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The following context can also be helpful to differentiate between those two terms:
با معرفي روش «سيمهاي مستقيم» توسط دکتر «اندرو» که بهعنوان نسل اول اين روش شناخته ميشود، حدود 4 دهه قبل، روشهاي درماني ارتودنسي دچار تحول شگرفي شد. اين روش بر پايه نقش کليداکلوژن بنا شده بود. در اين روش با حذف استفاده از خم کردن سيمهاي ارتودنسي، از سيمهاي آماده و پيشساخته بدون نياز به خم، درون شيار براکتها استفاده ميشد و تعيين موقعيت دندانها با توجه به پيشبيني زواياي مربوط به هر يک از آنها در براکت مربوطه انجام ميگرفت
براکت is called "bracket" in English and differs from braces. Would you please reread the definition of "dental braces" provided in wikipedia? Braces refers to the device as a whole, while brackets are one of its components. I would also like to give you two sentences from Wikipedia to prove my claim that bracket differs from brace:
1) In the case of traditional metal or wire braces, one uses brackets, bonding material, arch wire, and ligature elastic, also called an “O-ring” to help align the teeth.
2)Traditional braces are mostly used in treating children, as well as, adults. They consist of a small bracket that is glued to the front of each tooth and the molars are adjusted with a band that encircles the tooth.
The following link is also informative since all the components of this device has been explained with their English equivalent. http://www.draliheidari.com/20
Hope my explanation has been clear to illuminate the difference.