There is really no difference, but today, "apps" are seen as something you buy and/or download from an online store that will work on multiple devices. "I'm going to download that app.. it costs $1.99 and will work on my tablet and phone." This has become a popular term because of the rise of tablets and smartphones. For example, "Modern UI" apps are programmed in Visual Studio in C#, have cross-compatibility between devices, and usually incorporate web scripting elements.
Applications is an umbrella term (now) that includes Store APPs, as well as other more traditional, customary software and programs. Much is just semantics. Used to say, "All Programs", now says, ALL Apps....same, really. Still says "Programs & Features" but, installed programs show listed as ALL Apps. Oh and sometimes we refer to things as Utilities and list them, also, under Programs or is it Applications? Confused yet?
All software are programs but not all programs are apps according to my definitions. The diagram is a simple view which is capable of more or less unlimited expansion but which I use to differentiate system software (used to drive the system), applications software (for the end user to run) and utility software (to maintain the system).