What is the difference between Wajib and Fard? And why is there a dispensation for shaving the beard, even though shaving it is impermissible, while the hijab is Fard and there is no dispensation for removing it? And why do the dispensations for shaving not apply to removing the hijab?

The terms fard (obligatory) and wajib (necessary) are synonymous according to the majority of scholars, and they refer to what the Lawgiver has made incumbent. However, according to the Hanafis, fard is that which is established by a definitive proof, while wajib is that which is established by ajectural proof. Growing the beard is wajib according to the majority of scholars, whereas the Shafi'is differed on it, oscillating between obligatoriness and dislike (makrooh). The allowance granted by some scholars for trimming the beard does not stem from a relaxation of wajib over fard, but rather from their reliance on the permissibility of taking what exceeds a fistful, or trimming it during rituals (nusuk), or from the view of those who consider shaving disliked (makrooh) but not forbidden (haram). The hijab is fard (or wajib) for a free, adult woman.