In TOS, unlike in TMP, Kirk's affection for the Enterprise seems more tied to his sense of duty and dedication to the "star service", much like his literary antecedent. Horatio Hornblower longs for the sea, a sense of duty and purpose, which is usually expressed in terms of his affection for his ship regardless of name. Doesn't matter to him if it is the Hotspur or Lydia or Sutherland. It is what the ship connotes for men like him--adventure and service.
Kirk isn't so much in love with the Enterprise as he is in love with his career. Therefore, the Enterprise represents the pinnacle of his achievement. After all, in TOS, we are often told that it takes a rare breed of men to command a starship.
Later, this affection is transmuted into a "love affair" in the Trek films.