When you're starting out, it is tough to make sense of all the terminology, like "posts," "pages," etc. Take a look at the Pages article in the Codex. It does a better job than I can of explaining the difference.
Pages are what show up in most theme's main menu, as you've discovered. While it is possible to create a custom template that lists all the posts from a category and assign it to a page, so you could accomplish what you describe, an easier and more common way to accomplish it in WordPress is to create Categories of "New Cars" and "Old Cars" (Posts -> Categories), then assign the corresponding articles to those Categories.
Next, if your theme supports widgets, go Appearance -> Widgets, click on the "Categories" widget, and drag it into one of your theme's Widget Areas. The Categories widget will list your "New Cars" and "Old Cars" categories, as well as any others you create, in the widget as links to pages containing just the posts in those categories.
If you want more control over the order of the categories in the widget than the Categories Widget allows, you can instead create a custom menu (Appearance -> Menus) based on the categories you created, then use the Custom Menu widget to place the menu in one of your theme's widget areas.