Maybe the mics recording the audience or show were closer to the audience and/or 1000 plus people clapping is a high db level too. Maybe it was mixed for this effect. Good question.

Because the microphones are generally in or close to the audience for classical music, or for rock music, there is the fact that there are hundreds if not thousands of people clapping and screaming (hopefully). Also, many live recordings of pop music also have a mic or two pointed towards the audience to ensure the recording has a live feel.

This is why we are called Audio Engineers. It really depends on many different situations to control applause. Generally, fine arts recordings of symphonies/orchestras & other classical music doesn't generally have raucous audiences. Whereas, with many pop acts you have raucous & screaming fans. So when you are doing live rock 'n roll recording, this is the reason why we tight mic everything on stage with mostly dynamic cardioid microphones. I've recorded plenty of rock 'n roll groups with 65,000 screaming fans in football stadiums where the 65,000 people are almost hard to hear unless you include some audience capture microphones. Your problem is also another reason why I don't record rock 'n roll groups with a stereo pair of microphones to record a PA system for any kind of rock 'n roll recording or other popular genres. In fact, at the end of songs, I frequently had to bring up the audience mics to add the proper excitement. In fact without those audience microphones, even with 65,000 screaming fans, a live rock 'n roll recording made without the audience microphones almost sounds like it was done in a soundproof studio! And so this is really a matter of experience, technique & knowledge. Of course, when I have been invited by some of my friends to rock 'n roll concerts (because they wanted a bootleg recording) I had to use a pair of Omni directional "tie tack/lavalier", draped over my ears with a battery-operated pocket-sized DAT recorder back in the day. Those recordings had overly loud audience applause which had to be dealt with when Mastering the stereo recording. Without doing that, applause levels were louder than the music which is just too obnoxious. And I'm already obnoxious enough. But then everybody here already knows that.

I'm another obnoxious audio guy
Mx. Remy Ann David

I've recorded a lot of theater shows that our local community theater group produces. The theater holds 250 or so, and the group can't afford wireless mics for the performers, so miking consists of a couple of SDCs hung from a catwalk above the audience and pointed at the stage.
Works fine, but the applause becomes overwhelmingly loud... to counter this I run the two mics through a compressor with some pretty high ratio above a moderate threshold. Does nothing on the dialog, but holds the applause in check and makes for a much more palatable listening experience. I use the cheapest of all compressors (Alesis 3630... this is the ONLY use this unit ever sees, I wouldn't recommend it for anything else, really). The mics are typically my Rode NT3s as they're about the only condenser mic I'll let out of the studio for on-site work of this nature.

In other settings, like a live band performing, I echo what Remy says... I put an omni up to record the room, everything else is close mic'd or DI'd, heve to actually bring the omni track up into the mix to add the live ambience.

But to answer the OP's question, the audience sounds so much louder because they ARE louder! Manny many voices and hands clapping will move a lot more air than the performers on stage.

Jeff

As thatjeffguy indicated he uses a couple of small diaphragm condenser microphones hung from the catwalk at his local community theater. And he has problems with the audience being too loud. I have found that in these situations, this can also be due to the condenser microphones higher level of sensitivity & broader response range than a dynamic SM57. What people don't realize is is that an SM57 can work better for him than a condenser microphone. And if you feel the 57 is not up to the specifications task? Look and you will find that there are other fine dynamic microphones that can virtually outperform any cheap condenser microphone. The biggest difference you'll hear is that the dynamic microphone will be less adversely stimulated by the ambient environment, which equates to better control, more focused sound, less noise. And a 57 plugged into a quality preamp will sound way better than a cheap condenser microphone into a crispy crunchy preamp that supposedly is "cleaner & more transparent". This identical situation cropped up about 10 years ago. My Remote Truck and myself were for a time associated with the largest recording studio in the state of Maryland called Omega. Omega was not only the largest studio in town but also at the time the second-largest independent recording school in the nation, next to Full Sale in Orlando Florida. We take my truck out to record a gospel job and all of the in-house teachers/engineers were trying to put fine quality Neumann condenser microphones on the choir. Problem was is that the drum set sat right next to the choir. The engineer/teachers couldn't get the proper mix/balance and they were wearing out the choir prior to the show. I told them that we need to hang 57's instead of those Neumann's. Their response was "we really need higher-quality than those can deliver..." Bull! Those are the microphones to use. Especially because of their troubled situation. And they learned that right quick. In fact they were really amazed at how much better those 57's sounded than they expected. DUH Of course they sound good, they were plugged into my Neve which have marginally good preamps. Really it's because I know better since I specialize in this and I have been a broadcaster. So I had to teach the teachers! It was the blind leading the blind and that's what I don't like about recording schools per se. Back then they also taught folks that ribbon microphones were noisy and you shouldn't use them for just that reason. Love that kind of quality information. I hope they are eating their ribbons right now. Hell they didn't even have any in a multi-million-dollar studio. Nothing like combined stupidity always winning out.

Of course there is something to be gleaned from any form of additional education. No matter how bad that information might be. Religion is a good example of that. Everybody needs it but not everybody needs it. What we're talking about here is my religion, music. It's a universal religion accepted by all. So we are really further ahead in the game here than most other places in the world. And that's because we believe in music. At least most of us.

All the music & religion I listen to has a melody
Mx. Remy Ann David

Remy, these are some good thoughts. I haven't tried my 57's in this situation. My concern would be twofold, and I would value your opinion on this (mind you 99% of my recording is done in-studio, I defer to your experience, especially in the location-recording arena!).
My concerns would be 1.) Will the 57's be sensitive enough to pick up the actor's dialogue over a distance approximating 30' and 2.) Will my FF800 interface provide enough gain to boost the lower output of the dynamic mics to a useful level?
Thanks for your thoughts,

Jeff

Another perspective: The entertainment business is 95% (or more) about creating an illusion.

The artist, or label, wants the listener to buy into the illusion that their band is the most exciting live show EVER and everyone is in reverent silence during the song. Then as the last note rings out, their fans take a moment to wipe away their tears and erupt in deafening levels of cheers and applause because they are that excited and grateful to be there to witness their musical genius.

In post-production the mixing engineer can cheat this all day long fairly easily and make a crowd of 1,000 genuinely enthusiastic fans sound like 100x that. Not only can they push up the volume of the crowd mics and add delay/reverb to make it sound like a bigger venue than it actually was. They can layer in some of the loud applause from the encore and other samples from the same show - or other shows recorded from the same tour. And I wouldn't put it past them to take applause from someone else's recorded show.

(oh yeah, and a lot of that crowd noise is in a place your speakers and ears are fairly sensitive)

Yeah, the illusion is that only expensive microphones & other equipment will give you the illusion you want. That's an illusion. Look! A chicken! So, Mr. Hawk, they're trying to make less of the applause not more. The question is how to tame the over raucous nature of an over exuberant & appreciative response. Most men & women always think things should be bigger. But it's really better sometimes when they're smaller. It doesn't hurt... Your hearing, that is. Maybe your wallet? Your feelings?

Buck Buck Buck cluck
Mx. Remy Ann David

I always normalize/limit the applause sections before normalizing the entire file.