No, they have to have happened differently too. For example, in "Balance of Terror" we wouldn't have the conversation where Spock explains cloaking devices to Kirk and nobody would be surprised by them because only 10 years ago they were widely known. "Yesteryear" would have played out somewhat differently because Spock had a human sister he was raised with. "Wrath of Khan" would end differently because starships have big windows out front, negating the visual static issue. Spock starts acting crazy in "Amok Time"? Ring his sister and ask her what's going on. Raised on Vulcan, she'd be Starfleet's foremost expert on a people who were largely mysterious in TOS. She knows all about melding, Katras and many other things the classic crew didn't.
ENT was a century before TOS, and an effort was made to show technology progressing from current-day keyboards and Windows-style GUI's toward jelly beans and blinking coloured squares. Time travel (with 2 or 3 cases where it's explicitly said that history has been altered) excuses the continuity hiccups.