Rape is violent and does not have consent of both parties. Surprise sex has the consent of both parties.

If a woman says, "No" "Stop!", pushes the man off her, is struggling, and doesn't give complete consent, it's rape. If a woman is participating and likes it, just as much as the man, then it is surprise sex. There's a very big difference.

That would insinuate that all rape is done 'all of the sudden'.

Rape is also any kind of sex done without the consent of someone, or done with or without the consent of someone ineligible to give consent.