Equivalence of two lambda expressions for NOT
In order to prove the two NOT forms are not generally equivalent, all you have to do is find a term that when each is applied, returns a different result such as:

$NOT1 \; \lambda x.\; x \; \;\;=\;\; (\lambda x. \; x \; (\lambda t.\lambda f.f) \; (\lambda t. \lambda f. t )) \; \lambda x.\; x \;\; =\;\; \lambda x. \; x \; $

$NOT2  \; \lambda x.\; x \; \;\;=\;\; (\lambda x.\lambda t.\lambda f.xft)  \; \lambda x.\; x\;\; =\;\; \lambda t.\lambda f. ft \; $