What kind of stem is this?

[Heifzilla]

This is a picture of my stem. It is one piece, and as you can see I have it set too high (those marks are minimum insertion marks) . Since I like where it is and it's too short at the minimum insertion marks, I am going to have to get a new one.

I just have no idea what kind of stem this is. There's a rubber cap on it and a nut down at the bottom inside that I loosened to pull them stem up to where it is. When I do a search for bike stems I get just the section that holds the handlebars, but not the more vertical part that looks like what Sheldon Brown calls a stem quill? Is this a low-end bike thing or something that was done 12 years ago (that's how old the bike is) or what? And what do I need to get to replace this with something taller? I am woefully ignorant on proper terminology, so I apologize in advance for not having a clue what I am talking about here

I labeled the picture Can someone please tell me if I have the parts correct? If I want to replace this, how do I go about doing it? Thanks!

Edit: ok, I *think* what I have is called a quill stem and I'll either need another quill stem that is taller or I need to get a threadless adapter if I want to use those other types of stems I see on more "modern" bikes than mine (Aheadset?). Am I right? This sure is a learning experience. I feel like I should be sitting on my porch waving my cane and yelling at the youngins to "git off my lawn!" because I feel like I'm old and behind the times