Gaming laptop, or a thin laptop plus a desktop at home? Which makes more sense?

Desktop plus thin laptop, easily. A desktop can be upgraded part by part for years. A gaming laptop is mostly a sealed bundle: the graphics chip and processor are usually soldered, you can swap memory and storage and that is it. The thin laptop will also last longer in a bag. The price you pay is two machines to maintain and having to sync your files between them.

@Dmitri agreed on the sealed graphics chip. Tyler's memory question is the one to settle early: for coursework and coding, how much you need depends on what you run, and the linked thread covers it. I would favour more memory in the thin laptop if you can add it, because that is the part most often soldered in thin machines. Check the spec sheet for whether it can be upgraded.

I did the one-laptop route because my room is tiny and I could not fit a desktop tower. It works, but I plug it into a stand and a monitor and it basically turns into a desktop at my desk. The downside I notice is that the fans are loud, so I use headphones.

Tyler, one thing people leave out: thermals. A thin laptop cannot cool a powerful graphics chip, which is why gaming laptops are thicker and why they are louder. If you pick the thin laptop plus desktop route, you get a quiet bag machine and a desktop that can have a proper cooler. If you pick the gaming laptop, check how its fans behave under a long session in reviews from reputable test labs, not just the spec sheet. The same chip name can behave very differently in different chassis.

For us, downtime is the argument. If your only machine breaks the week of a deadline, you have nothing. Two machines means one can cover the other. That is why we avoid single points of failure in the office. It is also why I would keep the desktop at home and not tie everything to one laptop.

@Dmitri that is the honest answer I was hoping for. The part about the sealed graphics chip is what I had not thought of. How much RAM would you put in the thin laptop for school and coding? There is a thread on how much RAM a laptop needs but I would like opinions here too.

Used market angle, since it is my day job: gaming laptops lose a lot of their usefulness once the battery and the cooling age, and the dust gets into the fans. A desktop's parts keep their usefulness and can be moved to the next build. Also, the right-to-repair situation is better on desktops, because a failed part is replaceable on its own.