Levothyroxine is wholly synthetic and is made in a factory.
NDT is natural dessicated thyroid. It starts off life being the thyroid of a pig. Lots of pig thyroids are pulverised and dried. Then fillers are added, and the dessiccated thyroid gets made into pills. A pharmaceutical chemist would probably laugh his socks off at my description, but its how I always imagine it happens.
You can go to a supermarket and buy pork chops, pig liver, pig heart, pork sausages etc, but buying pig thyroid pills is not possible. It is classified as a prescription-only medicine, just like levothyroxine.
Levothyroxine contains only one thyroid hormone, referred to as T4.
NDT contains all the thyroid hormones that a mammal thyroid makes - T4, T3, T2, T1 and calcitonin, and any hormones or other substances that have yet to be discovered. The proportions of the different thyroid hormones in the thyroid differs between species, and doctors often use this fact to claim that pig thyroid is very bad for us so we shouldn't take NDT. Instead we should take 100% T4, 0% T3, 0% T2, 0% T1 and 0% calcitonin plus 0% of all the unknown hormones they don't yet know about in levothyroxine pills.