Chrome App - Chrome Apps are really just websites that allow you to accomplish a certain task. If I wanted to create a video on my Chromebook, I could go to WeVideo.com or click the App for WeVideo. Downloading apps from the Chrome store allows us to have quick access to websites that we use on a regular basis. Apps are categorized in the Chrome store. This helps me when I am searching for a good website/app to use for a specific purpose. **Note: Apps now also include many offline-capable applications that work similarly to traditional PC or MAC programs- opening as a separate window. You can find these under "For Your Desktop" and they're also marked with a lightning bolt in your search results**
Chrome Extension - A Chrome extension gets it name because it actually extends your browser's capabilities across many websites. These capabilities could be anything from taking a screenshot, creating a screen recording, having text read to you, etc. For example, I used a Chrome extension called Webpage Screenshot to take the screenshot you see in this post and to annotate that screenshot. That extension works no matter what webpage I am on.