Why is Selenium IDE called IDE when it is just a Firefox Browser extension?

That is because it is used to record what we're doing inside the browser. A recording will effectively trace each step of what we want to do on a web page. While recording, it will generate Selenese, or basically the script of things that you did while in record mode. The script is referred to as Selenese, but it really isn't just a dialect, it's more of a cobbled-together bunch of commands that are generated from our unit tests. Once we have our Selenese, we can then playback that script, and it will have automated the tasks that we did on that page, or even multiple pages, to get to that point. This type of testing is often referred to like record and playback testing.