Shots of Me's profile on iTunes says that it's "time for something new" – implying that it's offering something different in comparison to its well-established competitors such as Instagram, SnapChat, and even Twitter.
At first glance, it doesn't appear to be that different. The features listed by Shots of Me boast being able to "double-tap [a] selfie that you like" and "share a selfie" and "browse the real-time feed" which doesn't appear to differentiate itself from Instagram in the slightest.
However, Shots of Me is different as it does exactly what it says on the tin: it's meant be exclusively for selfies. The app only allows you to use your front-facing camera, discouraging shots of people's food and pets. Plus, there aren't any filters to magic away bad lighting or to make your face appear more "arty".
Shots of Me allows users to tag their friends in photos, add hashtags, a caption, and even your location. You can choose to tweet your photo, and there's currently an Instagram icon with a "coming soon" badge over it, so it appears that you'll soon be able to push your Shots of Me selfies to your Instagram feed.