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This paper studies the coherent and non-coherent multiuser multiple-input multiple-output (MU-MIMO) uplink system in the finite blocklength regime. The i.i.d. Gaussian codebook is assumed for each user. To be more specific, the BS first uses two popular linear processing schemes to combine the signals transmitted from all users, namely, MRC and ZF. Following it, the matched maximum-likelihood (ML) and mismatched nearest-neighbour (NN) decoding metric for the coherent and non-coherent cases are respectively employed at the BS. Under these conditions, the refined third-order achievable coding rate, expressed as a function of the blocklength, average error probability, and the third-order term of the information density (called as the channel perturbation), is derived. With this result in hand, a detailed performance analysis is then pursued, through which, we derive the asymptotic results of the channel perturbation, achievable coding rate, channel capacity, and the channel dispersion. These theoretical results enable us to obtain a number of interesting insights related to the impact of the finite blocklength: i) in our system setting, massive MIMO helps to reduce the channel perturbation of the achievable coding rate, which can even be discarded without affecting the performance with just a small-to-moderate number of BS antennas and number of blocks; ii) under the non-coherent case, even with massive MIMO, the channel estimation errors cannot be eliminated unless the transmit powers in both the channel estimation and data transmission phases for each user are made inversely proportional to the square root of the number of BS antennas; iii) in the non-coherent case and for fixed total blocklength, the scenarios with longer coherence intervals and smaller number of blocks offer higher achievable coding rate.