Mean Square Error vs. Squared Error Loss

Hi, I'm trying to reconcile in my head what seem to be differences
between Mean Square Error and Squared Error Loss. These terms seem to
often be used interchangeably, however every definition I've found for
MSE describes it as being composed of 2 components: bias and
variance. This is straightforward, however some papers,
http://www.ics.uci.edu/~pazzani/Publications/MLJ97.pdf
pg113 eq.(8)

define Squared Error Loss in the same way as MSE:
Variance(estimator) + (Bias(Estimator,Estimated))^2 [or the
equivalent variant of this]

but then go on to describe it as being canonically decomposed into 3
parts, the intrinsic error due to noise in the sample, the statistical
bias (error from an infinite sample) and the variance (error to the
sample's finite size).

Although the explanation of these 3 components seems intuitive, I
cannot seem to find an explanation/definition which breaks the MSE/
Squared Error Loss down into these 3 components in equation form.

What is the relationship between these 3 components and the 2
components (bias and variance) which are typically used in MSE
definitions? Or, how does the intrinsic error figure into the
equation (I'm assuming this is the bit missing from the usual 2
component description, or that it typically subsumed by one or both of
the bias and variance). Or what is the difference between MSE and
Squared Error Loss?

Thanks much.
.

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