Addressing the question in the title:
The Hebrew phrase b'nei Yisrael refers to Jews (the sons of Jacob and all their descendants -- plus converts even though they technically aren't sons of Jacob). You usually see it in this form -- Israel, not Jacob. The only Tanakh uses of b'nei Yaakov (Jacob) I can think of are either referring to his sons specifically (genealogy) or poetic pairings with Yisrael (in Psalms, particularly; example in the edited question).
I suppose b'nei Yisrael would also refer to Jews who converted out (e.g. to Christianity or Islam). It wouldn't refer to gentile members of those religions, since they are not descendants of this family.
From what I've been taught, poetic repetitions aren't meant to describe exclusive sets; "chidren of Jacob" does not describe a completely different group than "children of Israel". The recasting/repetition is done for poetic effect or to bring some more-nuanced meaning. Another example of this is in Deut 32:1 at the beginning of Moshe's final song, where it says "give ear...listen". I don't know a lot about biblical-poetic constructs, so I can't elaborate more on this. (That might be a good separate question.)
As for what the English phrase in a song lyric could mean, I don't think this site will be able to help.
Please note: This answer was written for a neutral, academic audience
and is not intended to be interpreted in the context of a religious
belief or doctrine.