Apps are generally programs meant for mobile devices, whereas programs are meant for computers running a regular OS like Windows, macOS, or Linux. However, within the past 6 years or so, there has been a push to bring apps to the desktop environment. Both Microsoft and Apple have app stores on their systems that allow you to download compatible apps to your computer. Apps are generally distributed through a centralized source (like the Microsoft Store app or the Apple App Store app) whereas a typical desktop program you have to download from the manufacturer of the program.
Microsoft has something called UWP (Universal Windows Platform), which allows developers to make apps that run on different platforms (W10, Xbox One, Windows Phone 10, HoloLens) without having to make separate versions for those platforms. One app built with UWP can run on all of those platforms.
As far as I'm aware, Windows 7 cannot run any Windows 10 apps.