Sensory cortex exhibits highly variable responses to the same stimulus across trials. This variability is correlated across neurons. The pattern of correlated variability is important because it informs us about stimulus encoding and the underlying structural connectivity. In visual areas, it has been shown that correlated variability depends on orientation tuning. However, it is challenging to interpret this tuning dependence when the spikes are generated from a doubly stochastic Poisson process, which is commonly assumed. In this case, spikes can exhibit tuning-dependent noise correlation, even if the noise correlation of the underlying firing rate is tuning-independent. Furthermore, a diverse set of tuning-dependent patterns can be explained by adjusting tuning-independent multiplicative and additive noise in the firing rates. We investigated how noise correlation and covariance of simultaneously recorded spikes from V1 and V2 depend on orientation tuning. Affine models with tuning-independent multiplicative and additive noise fit separately to V1 and V2 capture the observed tuning dependence of the correlations both within and between areas. Moreover, we carry out a simple derivation of noise correlation that provides an intuition for the observed patterns. We show that the additive noise within V1 is not correlated with the additive noise within V2, whereas the multiplicative noise is correlated across areas. To investigate the underlying circuit mechanisms, we simulated a stabilized supralinear network with a ring architecture representing a single area, receiving external input. We find that both multiplicative and additive noise emerge in the network when the neurons only receive additive noise in the input. Interestingly, only the additive, but not the multiplicative, noise is correlated with the input noise. Our results demonstrate that tuning-independent multiplicative and additive noise are sufficient to explain the tuning-dependent correlated variability within and between V1 and V2.