No. I've seen many peppers, and that does not look like a chile pepper (granted, I've seen a few peppers that I didn't think looked like peppers while young—e.g. my greenhouse-grown Aji Omnicolor peppers; the indoors one looked like a regular pepper, however). Your plant looks more like basil, but I don't really know what it is. It doesn't look like a pumpkin or potato plant.
Pepper leaves typically are not serrated. They're usually broader (although that can depend). They're usually somewhat thicker (those leaves look thin). The new leaves grow differently. Pepper stems usually look tougher (that one looks very pliable).
If that's basil, you should be able to identify it by smell and/or taste (if you know what basil smells or tastes like—but be careful not to swallow, in case it's an unidentified poisonous plant). There are many kinds of basil (and many taste or smell different), however. The most popular ones have broader leaves than that, but some, such as various kinds of Thai basil, have narrow leaves. Possibly Spicy Globe basil.
The other pictures should help us identify it better.
A green chile is just a green hot pepper (not a specific variety, either). Green peppers are normally unripe, although they may be fit to eat at a certain point while green; so, the plant won't normally have green in the name, and if it ripens red, as most peppers do, it's no more a green chile plant than a red chile plant. However, some peppers may be better suited for green picking, even if they ripen red—so take what I said with a grain of salt.
If what you have is a chile pepper, the leaves probably are spicy (or contain some capsaicin), too. Some pepper breeds have leaves that are supposed to be edible, but I have no idea which ones. (So, I don't recommend swallowing that or leaving it in your mouth long if you try it.) However, Spicy Globe basil and other plants may or may not be spicy, too (but probably in a way that feels different).