The Alter Rebbe defines chokhmah, binah, and da'at as three distinct intellectual faculties of the soul's intellect (sekhel): chokhmah is the flash of insight, binah is the full analytical development of an idea, and da'at is the deepest faculty — the intimate bonding and internalization of the idea into one's very being, described as the 'sinews' that bind the intellect to the heart.
וּכְשֶׁמּוֹצִיא כֹּחוֹ אֶל הַפּוֹעַל, שֶׁמִּתְבּוֹנֵן בְּשִׂכְלוֹ לְהָבִין דָּבָר לַאֲשׁוּרוֹ וּלְעָמְקוֹ, מִתּוֹךְ אֵיזֶה דְּבַר חָכְמָה הַמּוּשְׂכָּל בְּשִׂכְלוֹ – נִקְרָא ״בִּינָה״. וְהַדַּעַת, הוּא מִלְּשׁוֹן ״וְהָאָדָם יָדַע אֶת חַוָּה״, וְהוּא לְשׁוֹן הִתְקַשְּׁרוּת וְהִתְחַבְּרוּת, שֶׁמְּקַשֵּׁר דַּעְתּוֹ בְּקֶשֶׁר אַמִּיץ וְחָזָק מְאֹד, וְיִתְקַע מַחֲשַׁבְתּוֹ בְּחוֹזֶק בִּגְדוּלַּת אֵין־סוֹף בָּרוּךְ־הוּא, וְאֵינוֹ מַסִּיחַ דַּעְתּוֹ. כִּי אַף מִי שֶׁהוּא חָכָם וְנָבוֹן בִּגְדוּלַּת אֵין־סוֹף בָּרוּךְ־הוּא, הִנֵּה אִם לֹא יְקַשֵּׁר דַּעְתּוֹ וְיִתְקַע מַחֲשַׁבְתּוֹ בְּחוֹזֶק וּבְהַתְמָדָה – לֹא יוֹלִיד בְּנַפְשׁוֹ יִרְאָה וְאַהֲבָה אֲמִיתִּית, כִּי אִם דִּמְיוֹנוֹת שָׁוְא.
When one brings forth this power from the potential into the actual, that is, when [a person] cogitates with his intellect in order to understand a thing truly and profoundly as it evolves from the concept which he has conceived in his intellect, this is called binah. Daat, the etymology of which is to be found in the verse, “And Adam knew (yada) Eve,” implies attachment and union. That is, one binds his mind with a very firm and strong bond to, and firmly fixes his thought on, the greatness of the En Sof, blessed is He, without diverting his mind [from Him]. For even one who is wise and understanding of the greatness of the En Sof, blessed is He, will not—unless he binds his knowledge and fixes his thought with firmness and perseverance—produce in his soul true love and fear, but only vain fancies.