  Cosmological analyses of second-order weak lensing statistics require precise
and accurate covariance estimates. These covariances are impacted by two
sometimes neglected terms: A negative contribution to the Gaussian covariance
due to finite survey area and the super-sample covariance (SSC) which for the
power spectrum contains the impact by Fourier modes larger than the survey
window. We show here that these two effects are connected and can be seen as
correction terms to the "large-field-approximation", the asymptotic case of an
infinitely large survey area. We describe the two terms collectively as
"Finite-Field-Terms".
  We derive the covariance of second-order shear statistics from first
principles. For this, we use an estimator in real space without relying on an
estimator for the power spectrum. The resulting covariance does not scale
inversely with the survey area, as naively assumed. This scaling is only
correct under the large-field approximation when the contribution of the
finite-field terms tends to zero. Furthermore, all parts of the covariance, not
only the SSC, depend on the power- and trispectrum at all modes, including
those larger than the survey. We also show that it is generally impossible to
transform an estimate for the power spectrum covariance into the covariance of
a real-space statistic. Such a transformation is only possible in the
asymptotic case of the "large-field approximation".
  Additionally, we find that the total covariance of a real-space statistic can
be calculated using correlation functions estimates on spatial scales smaller
than the survey window. Consequently, estimating covariances of real-space
statistics, in principle, does not require information on spatial scales larger
than the survey area. We demonstrate that this covariance estimation method is
equivalent to the standard sample covariance method.
