OK, in the other games I've plaid (mostly MMORPG's but what the heck) there was a clear distinction between this things.
Competitions were contests where players erm... competed with other players in some aspects of the game, like fighting. For example, in Runescape there were clan wars, where everybody with a clan could participate. Yes, high-leveled players with huge high-leveled clan had the upper hand, but considering the dedication they had for the game, having and advantage is only normal.
On the other hand, events were usually happening during holidays and were like mini-quests rewarding a fancy item, which was just looking awesome. Also fan sites also conducted events, like having people with Halloween masks walk through the entire world. This didn't include any competing.
So yeah, that's about what I had to say..