The term "app" has been coined to mean an accessory application on a mobile device (ie smart-phone or tablet), which I suppose can be extended to any device which is not specifically a work-horse computer (including STBs).
In general computing terms: a "program" is a single-purpose utility, whereas an "application" is more comprehensive such as word processing or graphic design (something which provides the entire working environment for a specific job).
I don't know how that helps the OP though.
How do you access Jazz FM
I don't have a FVP-5000T to refer to, but the Internet Radio app on the HDR-FOX seems easy enough to use:
TV Portal >> Internet Radio >> Search >> "Jazz FM"
...gets a list including "Jazz 98.5 FM" - no idea if that's what you want. You could also try the Category or Country listings.
A personal favourite of mine is "Polskie Radio - W jazzoym klimacie" (a seamless feed of jazz/easy, and not in Polish!).
...or even regional commercial stations such as Smooth midlands or east midlands?
Only stations which specifically provide an "Internet Radio"-compatible feed are available via an Internet Radio app. Smooth Radio is available on Freeview at LCN 718 (not regional, obviously).
If you are saying "Smooth Midlands" is available via a web page but not via Internet Radio, that just means they haven't provided the appropriate feed (or maybe not had it indexed). You have to remember web standards are always shifting, and mainstream browsers are always being updated (and becoming hugely bloated) to cope with them. Trying to put (and maintain) a full-featured browser onto an STB like the FVP would be a fool's errand.