

Hard to answer without some context. Got any examples for “formal website”?
In the fediverse an “instance” is any server which is running the software in question. For example, fosstodon is an instance of Mastodon. mastodon.social is also an instance of Mastodon.
So just a website?
Websites of all types are hosted by servers. These servers can run any kind of software they want in order to serve web pages to users. There are countless different options for server software (see just some of the options on Wikipedia: https://en.wikipedia.org/wiki/Comparison_of_web_server_software?wprov=sfla1), and they can run on different operating systems (Windows, Debian, Ubuntu, Fedora, macos, …). Two servers can serve very similar or even identical websites but run completely different software, and similarly, two servers can use the same software but serve totally different websites.
Basically it’s a free-for-all.