I do both. I have a custom built NAS based on a Ryzen 3600 and ZFS across 4 drives which runs about 20 self hosted applications and stores the majority of my files but its only accessible from within the home. I also rent a small VPS for personal webspace and hosting self hosted apps I want out of the house.
In the past I have also hosted raw servers from Hetzner or bigger VPS from Amazon for the purpose of hosting a game server. Alongside those I often had community applications like website, forums, wikis and custom chat and voice comms services.
Its all self hosting to me since I run it. The various options are all about the trade offs of security, accessibility, cost and performance. The cheaper cloud options when you add it up can be cheap compared to buying and running your own hardware when you take into account electrical costs and the likely hardware replacement needs within 5 years. The big cloud providers aren’t price competitive but Contabo/Hetzner really surprisingly are especially if you pay a lot for electricity. But then if you need a game server it can be quite hard to find good fast CPUs on the cloud and its not going to be 24/7 for communities, so the trade off flips back to having your own.
Since I got 1 gbit/s fibre internet my need for internal NAS has definitely reduced as the internet is nearly as fast as the local network so I could now have my NAS needs remote.