Pinching-antenna systems (PASS) represent an innovative advancement in flexible-antenna technologies, aimed at significantly improving wireless communications by ensuring reliable line-of-sight connections and dynamic antenna array reconfigurations. To employ multi-waveguide PASS in multi-user communications, three practical transmission structures are proposed, namely waveguide multiplexing (WM), waveguide division (WD), and waveguide switching (WS). Based on the proposed structures, the joint baseband signal processing and pinching beamforming design is studied for a general multi-group multicast communication system, with the unicast communication encompassed as a special case. A max-min fairness problem is formulated for each proposed transmission structure, subject to the maximum transmit power constraint. For WM, to solve the highly-coupled and non-convex MMF problem with complex exponential and fractional expressions, a penalty dual decomposition (PDD)-based algorithm is invoked for obtaining locally optimal solutions. Specifically, the augmented Lagrangian relaxation is first applied to alleviate the stringent coupling constraints, which is followed by the block decomposition over the resulting augmented Lagrangian function. Then, the proposed PDD-based algorithm is extended to solve the MMF problem for both WD and WS. Furthermore, a low-complexity algorithm is proposed for the unicast case employing the WS structure, by simultaneously aligning the signal phases and minimizing the large-scale path loss at each user. Finally, numerical results reveal that: 1) the MMF performance is significantly improved by employing the PASS compared to conventional fixed-position antenna systems; 2) WS and WM are suitable for unicast and multicast communications, respectively; 3) the performance gap between WD and WM can be significantly alleviated when the users are geographically isolated.