Penalty rebounds: the post and goalkeeper are different
Why the original kicker can follow a save but not immediately follow a post rebound.
Another player must touch first
IFAB Law 14 says the penalty taker must not play the ball again until it has touched another player. A goalpost or crossbar is not a player. A goalkeeper is.
For a hypothetical ordinary in-match penalty that hits the post and returns directly to the kicker, an immediate second kick breaks this requirement. If the goalkeeper touches the ball first, that particular restriction is satisfied, although other rules can still affect the play.
A rebound does not always end live play
During normal match play, a saved penalty or one rebounding from the frame can leave a playable ball. The score has not changed just because the penalty was taken. A later valid finish is the scoring event.
Do not transfer this expectation to a penalty shootout. A shootout and a penalty within the match have different procedures; this guide focuses on the Law 14 in-match situation.
An end-of-half extension is narrower
When additional time is allowed only to take and complete a penalty, Law 14 defines when that kick ends. A touch by a player other than the defending goalkeeper, including the kicker, completes it. That is not an unlimited opportunity for a follow-up attack.
On a live score page, check whether the event is a penalty award, a saved attempt or a confirmed goal. Those labels describe separate stages. The hypothetical rebound examples here are explanations, not claims about a particular match.