Most rules in all ice hockey leagues will be the same. There will be a few differences based on the bylaws and goals of each league. In the NHL, icing can be waived off if it seems clear that the offending team would recover the puck before the defensive team. Most leagues I have played in, or officiated in have "automatic icing" which does not allow the offending team any allowance to prevent the icing. Also, offsides in the NHL is delayed until a player who is offsides directly influences play or touches the puck before the offsides have been cleared by the linesmen. In other leagues, there is no delay to offsides. Once a play is considered offsides, play ends until the puck is dropped to resume play.
In short, there are a few rules that are different, but most rules are the same.