Of course STID was a remake of TWOK. It's so obvious! Do I have to point it out detail for detail? OK, then:
-- TWOK: Kirk is 50-something, lamenting old age and questioning his confidence. STID: Kirk is 20-something and too cock-sure of himself.
-- TWOK: Spock has no real character issues. STID: Spock is full of issues.
-- TWOK: No Spock-Uhura relationship. STID: Spock-Uhura relationship.
-- TWOK: Khan is stranded on a hostile planet with the rest of his people. STID: Khan is essentially forced labor on Earth for Section 31 in order to keep his people alive.
-- TWOK: Carol Marcus is a molecular biologist. STID: Carol Marcus is a physicist and weapons specialist.
-- TWOK: Khan is obsessed with revenge against Kirk at any cost. STID: Khan is obsessed with freeing his people at any cost.
-- TWOK: Saavik is a major character. STID: No Saavik.
-- TWOK: Genesis device. STID: No Genesis device.
-- TWOK: Spock faces a no-win situation. STID: Kirk faces a no-win situation.
-- TWOK: No Admiral Marcus. STID: Admiral Marcus drives most of the conflict.
-- TWOK: Chekov has moved on in his career and is first officer on another ship. STID: Chekov becomes chief engineer on board the Enterprise.
-- TWOK: Kirk has a son. STID: Kirk has no son.
-- TWOK: No Pike. STID: Pike.
-- TWOK: Khan and Kirk never meet. STID: Khan and Kirk not only meet, they work together.
-- TWOK: Was about obsession (Khan with revenge), age, on-going friendship, death. STID: Was about maturing, growing friendship, obsession (Marcus with war), death.
There's probably more, but I think that's enough to convince anyone that STID was unoriginal and a complete rip-off of TWOK.