A recorded stand-up special looks like a single continuous performance and is normally assembled from two. The practice is driven by the risks of capturing live comedy once.
Live performance varies more than film does
A joke depends on delivery, timing and the room's response, and none of those repeat exactly. A performer can have an excellent night for one section and a flat one for another.
Recording twice creates two versions of every joke, which lets the edit choose the better one rather than accept whatever the single recording produced.
This is not a matter of fixing failure. Both shows are usually strong, and the edit is selecting between good versions rather than rescuing a bad one.
Technical risk is the second reason
A special is shot with multiple cameras and a full audio setup, and any of those can fail during a performance that cannot be paused or repeated.
A dropped camera angle or a microphone problem in one show is covered by the other, since the material and staging are effectively identical between them.
The audience is part of the recording
Laughter is recorded from the room and is essential to how the special plays, so the crowd has to be genuinely responsive rather than merely present.
Two shows on the same night produce differently energised audiences, with the later crowd often more animated, and the edit can favour whichever room served a section better.
Editors avoid cutting laughter in ways that misrepresent the response, since audio that does not match the visible audience is noticeable and undermines the performance.
Editing has to hide the seams
Cutting between two performances requires the staging, wardrobe and lighting to match precisely, which is why performers wear identical clothing for both shows.
Camera positions and the set are held constant for the same reason, and the running order is kept consistent so that material can be exchanged without disrupting the flow.
The material was fixed long before
By the time a special is filmed, the set has usually been performed for a year or more, and the order has been refined through repeated testing in clubs.
What is being captured is therefore a finished piece of work rather than an experiment, and the recording exists to preserve the best available performance of something already settled.
Comedians typically retire the material afterwards, which makes the recording the last performance of a set rather than a stage in its development.