Took the Tesla camping for the first time and wasn't sure which plug to bring

You don't need every adapter. For RV parks it's really two: the 14-50 (the 50A outlet) and the TT-30 (the 30A one). Each adapter tells the mobile connector what it's plugged into, so the car sets the amps by itself. Nothing to configure in the app. And yes, there's a huge difference. The 50A outlet is 240V, so with the Gen 2 connector you'll get 32A, roughly 7.5 kW. TT-30 is 120V. It's basically a beefier wall outlet.

Go with the 14-50 every time if the site has it. On the TT-30 you're adding maybe 3-4 miles an hour, which is fine overnight if you're sitting there a few days but useless if you're moving every day. One thing I'd add. Campground pedestals get beat to death. Half of them have breakers that have been tripping for 15 years and receptacles that are loose and scorched. I always knock the charge current down in the car to 24A or so on a pedestal I don't know. It takes a little longer, but I don't end up tripping the breaker at 2am, or worse, cooking the outlet. Also call ahead. Some parks charge an EV fee or don't allow it at all, and finding that out at check-in isn't fun.

To answer the question about the car figuring it out. The adapter has a resistor in it that tells the mobile connector what the circuit is rated for, and the connector limits itself to 80% of that. A 50 amp outlet gets you 40 amps in theory, but the Gen 2 mobile connector tops out at 32 amps anyway. The TT-30 adapter limits it to 24 amps at 120 volts, which is a little under 3 kW. You can always set the amps lower on the car's charging screen. You can't make it go higher than what the adapter allows, which is how it should be. I have a 14-50 at home and the outlet itself matters more than people think. If the plug feels warm after an hour, turn it down.

This is really helpful, thanks. So the 14-50 adapter doesn't come in the box? I thought I had one but all I can find is the regular household one

Depends what year you bought. They stopped including it a while back. It's around $45 on the Tesla shop. Worth it.

Get the 14-50 one even if you never camp again! Every RV park, plenty of farms and shops out here have them... it's the most useful adapter there is.

Also bring the 5-15 one you already have. I've stayed at a couple of tent sites where the pedestal had a 20A household outlet and nothing else. It's slow but it beats nothing.