Apps on my iPhone and Mac are not the same...?

When I purchase an app on my phone it does not show up in my itunes on my computer? The display of where all my apps are on my mac show that I have the app but it does not show that they exist in my library? How do I get the apps in both places? I will say though that the apps that I bought on my computer show up in both places, so no problems with that. Can anyone help?