A question for any Europeans/football fans. If this was hockey and teams (instead of football and clubs), I don't think anyone would say "They play hockey in two teams". It would be "They play hockey for (on, with) two teams". Do you play football for a club, or in a club? Or are club and team two completely different things in football? Thanks!
In my experience at least, you play for a club only if you represent the club against other clubs. If you represent the club, you play on the team against the other club's team. I'd interpret playing in a club or with a club as being less competitive, more for fitness or fun than matches. If someone bumps up their game and becomes good enough to play on the team, then they "make" the team. Team is the players on the pitch, club is the organisation to which they belong and train with. Sorry if this does nothing but add to the confusion :-P