Why do the rules of the post-prostration (sujud al-ba'di) differ between adding a surah to Al-Fatiha in the third rak'ah and adding a tashahhud between the third and fourth rak'ahs in a four-rak'ah or three-rak'ah prayer?

Increases in prayer are of two types:

1. Increase in Actions: An increase of the same kind as the prayer: Such as standing instead of sitting. This invalidates the prayer if done intentionally, but prostration of forgetfulness (sujud as-sahw) is performed for it if done out of forgetfulness. An increase of a different kind than the prayer: Such as walking or scratching. This invalidates the prayer if done in abundance, but a small amount is excused, and no prostration of forgetfulness is performed for it.

2. Increase in Sayings: That which invalidates the prayer if done intentionally: Such as uttering the greeting of peace (taslim) or human speech. That which does not invalidate the prayer if done intentionally: A prescribed remembrance said in the wrong place: Such as reciting during bowing (ruku') or prostration (sujud), or reciting an additional surah with Al-Fatihah in the third and fourth rak'ahs of a three-rak'ah or four-rak'ah prayer. Scholars differed regarding the prostration of forgetfulness for this; is it legislated or not? Some said: It is not legislated because the prayer is not invalidated by doing it intentionally. Others said: It is legislated, and it is recommended, not obligatory.

In summary: Adding a surah out of forgetfulness with Al-Fatihah in the third and fourth rak'ahs of a three-rak'ah or four-rak'ah prayer falls under the category of increases in sayings for which there is a difference of opinion regarding the legislation of prostration of forgetfulness. As for adding a tashahhud, it falls under the category of increases in actions for which prostration of forgetfulness is legislated by consensus.