This paper addresses the problem of quantifying the effect of noise induced error (so called variance error) on system estimates found via a regularised cost criterion. It builds on recent work by the authors in which expressions for non-regularised criterions are derived which are exact for finite model order. Those new expressions were established to be very different to previous widely used quantifications that were based on asymptotic in model order arguments. A key purpose of this paper is to expose a rapprochement between the new finite model order pre-existing asymptotic model order quantifications. In so doing, a further new result is established. Namely, that variance error in the frequency domain is dependent on the choice of the point about which regularisation is affected.