@Melooon @Noah_SI hope you don't think I'm horribly skewed for thinking some of these things, but that's kind of the way I'm seeing things as someone who is a week at coding. Please correct me on my assumptions, i'd like to have as clear an understanding as i can :)
Ok so you're not terribly far off I can totally understand what's confusing you based on what you said here.
A host: You are pretty much totally correct with this one; a host is a company or a service that hosts information or files on the internet.
A server: This is the actual computer that the host lives on, sometimes server and host are used interchangeably, but a host is more like a business, and a server is the building the business is in.
A service: Again this is like a business, a host offers service in the same way a a coffee shop offers a service. I would call GitHub or Neocities services that are also hosts.
An application or a program: These are things that run on your computer, e.g. code you have downloaded onto your computer and that lives and runs there. For example Photoshop, Word etc. (loosely speaking) Application / App is the Apple name, Program is the Microsoft name for the same thing.
Files: these are blocks of data that are stored on a computer (an image, a html file, a word document). They could be stored on your computer, or hosted on a server by a business (like OneDrive, iCloud)
Bandwidth: when you send a file over the internet, that travel uses bandwidth; if your files are like people in a city, bandwidth is the number of them that can fit on a train at once. When people say that an old website was overwhelmed by too much traffic, they are talking about bandwidth usage, not storage. - For a novice you prob don't even need to think about this.
~ So, you're confusion seems to be that many businesses offer services that host files, but also offer applications to interact with those files, and some of them save them to your computer, but others save them to a server. The thing is that these are actually all totally separate technologies that just happen to get bundled together by a lot of modern businesses. Its not helped by the buzz word "Web App" which basically means a website that offers application-like features, but there is nothing special about it, its still just a website.
Neocities for example is just a service/host, it has no application, and most web hosts would not have an application.
GitHub is a service that offers hosting built around a separate technology called Git; there are many applications that offer Git that you can install on your computer, but GitHub also offer their own custom one. You do not need to use GitHub to use Git, nor do you need to use the GitHub application to use GitHub

Traditionally Microsoft Office was just a program you installed on your computer, and it had no service or host involved; these days they do offer file hosting and online stuff as an extra, but the actual program is still just on your computer.
~~ It is frankly confusing, particularly if you grew up in a world post-internet where all these things are much more mixed up

The key thing to know for this thread is that an index.html file is just file, it can be stored on your computer (taking up a tiny bit of storage) or it can be hosted on a web server (host), like Neocities (which is a server, which is basically just someone else's computer)
Most "code heads" do both, they have their website files on their computer, and then they copy those files to their webhost when they are ready to allow other people to see them.
Your web host will never require a special application to edit a .html file, it can be edited in any text editor like, VSCode, or Notepad++, or it can be edited online using a service CodePen, or the Neocities editor. (Though I should note Word is not a text editor, its a formal document writer and cant be used for code!)
There are many ways to copy html files from your computer to your web host (github is a popular if ridiculously complex method used by neocities people way too often), but the easiest method is just to drag the files from your computer into your hosts file upload window - and that's fine for an amateur site.