In this paper, we investigate reconfigurable pixel antenna (RPA)-based electronic movable antennas (REMAs) for multiuser communications. First, we model each REMA as an antenna characterized by a set of predefined and discrete selectable radiation positions within the radiating region. Considering the trade-off between performance and cost, we propose two types of REMA-based arrays: the partially-connected RPA-based electronic movable-antenna array (PC-REMAA) and fully-connected REMAA (FC-REMAA). Then, we formulate a multiuser sum-rate maximization problem subject to the power constraint and hardware constraints of the PC-REMAA or FC-REMAA. To solve this problem, we propose a two-step multiuser beamforming and antenna selection scheme. In the first step, we develop a two-loop joint beamforming and antenna selection (TL-JBAS) algorithm. In the second step, we apply the coordinate descent method to further enhance the solution of the TL-JBAS algorithm. In addition, we revisit mechanical movable antennas (MMAs) to establish a benchmark for evaluating the performance of REMA-enabled multiuser communications, where MMAs can continuously adjust the positions within the transmission region. We also formulate a sum-rate maximization problem for MMA-enabled multiuser communications and propose an alternating beamforming and antenna position optimization scheme to solve it. Finally, we analyze the performance gap between REMAs and MMAs. Based on Fourier analysis, we derive the maximum power loss of REMAs compared to MMAs for any given position interval. Specifically, we show that the REMA incurs a maximum power loss of only 3.25\% compared to the MMA when the position interval is set to one-tenth of the wavelength. Simulation results demonstrate the effectiveness of the proposed methods.