I get income support because as a single mother i am deemed unable to look for work as i am the sole caretaker of my son. If i didnt have a child then i would be on JSA as i would be able to seek work. As far as i know the ammount you get paid is the same, it's just paid for by different departments.
Income support is for people with no income at all.
when i put savings into an account in my name 2 days before going to NY i also got a letter from my mother saying i was left this money by my grandmother who died a few years back and that she had invested it with her money so that i would get a higher rate of return. The consulate didnt ask about the lack of statements for that account, so didnt see my mothers statement, but im sure that i read somewhere that they wanted to see statements....im not sure though. That was just my experiance. Hope that helps.
Stay safe
Jules