Humans and robots are increasingly working together in human-robot teams. Teamwork requires communication, especially when interdependence between team members is high. In previous work, we identified a conceptual difference between sharing what you are doing (i.e., being transparent) and why you are doing it (i.e., being explainable). Although the second might sound better, it is important to avoid information overload. Therefore, an online experiment (n = 72) was conducted to study the effect of communication style of a robot (silent, transparent, explainable, or adaptive based on time pressure and relevancy) on human-robot teamwork. We examined the effects of these communication styles on trust in the robot, workload during the task, situation awareness, reliance on the robot, human contribution during the task, human communication frequency, and team performance. Moreover, we included two levels of interdependence between human and robot (high vs. low), since mutual dependency might influence which communication style is best. Participants collaborated with a virtual robot during two simulated search and rescue tasks varying in their level of interdependence. Results confirm that in general robot communication results in more trust in and understanding of the robot, while showing no evidence of a higher workload when the robot communicates or adds explanations to being transparent. Providing explanations, however, did result in more reliance on RescueBot. Furthermore, compared to being silent, only being explainable results a higher situation awareness when interdependence is high. Results further show that being highly interdependent decreases trust, reliance, and team performance while increasing workload and situation awareness. High interdependence also increases human communication if the robot is not silent, human rescue contribution if the robot does not provide explanations, and the strength of the positive association between situation awareness and team performance. From these results, we can conclude that robot communication is crucial for human-robot teamwork, and that important differences exist between being transparent, explainable, or adaptive. Our findings also highlight the fundamental importance of interdependence in studies on explainability in robots.