Everyone knows what first aid is, but what is second aid?

Second aid is the hospital
- They would do a way better job than me, they should probably go first
  
  Only when you're already in a hospital when the injury happens.
- The professionals.

First aid is what keeps the casualty alive long enough for second aid. Second aid is trained medical profesionals working in a medical setting, so a hospital or even the ambulace crew that take over after you stopped the casualty leaking too much.
- Yup. For minor issues, first aid is all that is needed; you don’t need to see a doctor for a minor cut, as long as the first aid ensures it’s not infected. But for larger things, secondary aid is what provides more long-term recovery.
  If someone dislocates a shoulder, first aid is putting it in a sling and bracing it against the body, so it doesn’t get worse (for instance, the tendons and ligaments in the shoulder joint can tear) before they can get to a hospital.
  If someone is massively bleeding, first aid is stopping the bleeding to keep them alive until they can get rescued.
- I would call the ambulence crew first aid. The hospital emergency room has a lot more equibment and staff. Sure the ambulence has more than you but their goal is still the same, get you to real help fast.
  
  So the box on the wall that says "first aid" is the ambulance crew, roger that

And at what point does Kool aid come in?
- When your antidepressants stops working 🙃
  
  Koolaid reminds you to use Flavor-aid in all your suicide plans
- It's a surprise. Don't stand too close to the walls

First aid is some random person that did a short class 10 years ago.
Second aid is a doc that studied for years but still doesn't have all the answers.
Third aid is when you call the dev. They won't pick up.
- God hasn't responded to a single one of my issues or merged a pull request since I started on this earth. Slacker.

Actually, the hospital/doctor is NOT what second aid originally is. And first responder aid is also not what first aid is about.
First aid is what is meant as the actual first aid that can be provided by anyone with minimal training. As the concept came from the military the "first aid" was meant to be applied by fellow soldiers - this is were the (rather surgical trauma oriented average first aid kit got most of it's content of). (Unit-level embedded medics came far later) In a civilan setting nowadays it includes the basic life support provided by non-specialist first responders and depending on the definition it might include BLS ambulances (which are not seen as professionals sometimes)
Second aid was what a medical professional does - a paramedic, corpsman or doctor and can also include a casualty collection post or similar structures. Definitions here split up a bit - depending on which authors you read second aid (aka the second aid stage) does not include any intrahospital care but does prolonged care scenarios(cases you cannot evacuate to a medical facility for longer times,like 24h+x). Other authors do include basic hospital care or similar facilities that provide some but not all treatment.
After that tertiary or definitive care takes over - that's when shit definitely gets fixed if it's fixable. That will always include intrahospital care.
To get back to your question what would be in a second care kit: Things needed for prolonged care usually. I did work in a prolonged care scenario for a while and can give you an overview what we had in our "prolonged care" kits: Urinary catheters (people need to pee even with a broken spine and we need to monitor urine production. And you can fix almost everything with it...you fix holes in hearts with them, can use them as a feeding tube,etc.), more and more permanent pain medication, suturing kits, surgical drainages,lots and lots of desinfectant, more iv fluids, heating solutions both for the patient and the fluids, medication for more permanent care (strong antibiotics, heparin to avoid pulmonary embolism from immobilisation), Military medics often include patient to patient blood transfusions kits, but I worked on the civilian side. These would easily enable one to care for patients for up to 72h hours. (Luckily 36h is the most I had to spend with a critically ill patient).
Source: Consultant paramedic.

Second aid is that person screaming "Call the ambulance!" when somebody already has.
- Somebody get a sponge.

Did you know there is last aid? It's a project, pretty much like first aid, that aims to educate as many people as possible about end-of-life care.
It's amazing and everyone should learn about last aid!
- Should probably learn first aid first, because we don't want people who only have last aid being first on the scene giving an ankle sprain last rites.

A flask of rum. If the first aid kit did or didn't do it then at least buzz it out.

Second aid is decade's of therapy to unpack the PTSD that happened to you

second aid
It is when you look at the situation for a second, and that's enough for you to understand that you can't help.

Go through his clothes and look for loose change.
- Nah that's when they are all dead. OP is talking about when they are mostly dead.
  
  He says he's not dead yet ..

The hospital. First aid is really just short for First Responder Aid.
It includes things that a first responder would do to stabilize someone so they can reach an actual aid station, like a hospital or medical encampment.
We don't call that second aid because that's not how we think about prioritizing things.
First responder aid is the unique side of things that needs to be called out separately, as it always has a role to play, even in a hospital setting. The people who arrive first administer first responder aid until you can be triaged and seen at the appropriate time to reduce the greatest risk to the most people. Which may mean you go to the back of the line, or it may mean they move you up to the front in a triage situation.

It contains chocolate!

Something to drink preferably water, some dextrose and magnesium and a blanket.

Posting a video.

The blues singer character Mississippi Gary from The Kids In The Hall comes to mind:
I got the blues so bad, I can't even close my eyes... I gotta call a friend on the phone and tell him - "Buddy, come over and shut my eyes for me, I got the blues".