In many speech recording applications, noise and acoustic echo corrupt the desired speech. Consequently, combined noise reduction (NR) and acoustic echo cancellation (AEC) is required. Generally, a cascade approach is followed, i.e., the AEC and NR are designed in isolation by selecting a separate signal model, separate cost function, and separate solution strategy. The AEC and NR are then cascaded one after the other, not accounting for their interaction. In this paper, an integrated approach is proposed to consider this interaction in a general multi-microphone/multi-loudspeaker setup. Therefore, a single signal model of either the microphone signal vector or the extended signal vector, obtained by stacking microphone and loudspeaker signals, is selected, a single mean squared error cost function is formulated, and a common solution strategy is used. Using this microphone signal model, a multi-channel Wiener filter (MWF) is derived. Using the extended signal model, it is shown that an extended MWF (MWFext) can be derived, and several equivalent expressions can be found, which are nevertheless shown to be interpretable as cascade algorithms. Specifically, the MWFext is shown to be equivalent to algorithms where the AEC precedes the NR (AEC-NR), the NR precedes the AEC (NR-AEC), and the extended NR (NRext) precedes the AEC and post-filter (PF) (NRext-AEC-PF). Under rank-deficiency conditions the MWFext is non-unique. Equivalence then amounts to the expressions being specific, not necessarily minimum-norm solutions, for this MWFext. The practical performances differ due to non-stationarities and imperfect correlation matrix estimation, with the AEC-NR and NRext-AEC-PF attaining best overall performance.