Question about background noise

I sort of disagree; you can have a very black background during vinyl reproduction, when all the stars align properly.  This is not to say there is NO noise.  This is to say that the signal to noise ratio of the system from front to back can be such that you hear silence at the listening position.  I admit this condition is not attained with every LP, only a few of the best.
Digital is indeed very quiet, but the trouble with digital is that as the signal voltage drops, you lose resolution, so Redbook CDs lack downward dynamic range; some of the extreme low level info is lost.  (Probably this problem is ameliorated with hi-rez downloads, but I haven't dabbled in that medium.)

The noise, or lack of noise, between cuts on an LP reveals any other source of noise other than the music, at the particular gain setting of the phono stage. Could be on the vinyl, could be the signal to noise ratio of your particular phono stage at that particular gain setting, could be due to any extraneous sources of noise in your system, like EMI and RFI. One thing I know: if I hear no inter-cut noise at my listening position, I am happy. If I hear "something", I try to think it through to determine what might be happening. Usually in those cases, I decide it’s nothing I can easily fix.

One phenomenon that could be operative in the OP's case is "bleed through".  This apparently can happen with masters made from tape or right on the LP, where the upcoming groove is heard through the groove being played.  I don't quite get the mechanism of the latter, but I do hear "pre-groove echo" on the odd occasion.  That is musical though.  I suppose it's even possible that electronic noise laid down in the studio is heard in between cuts.