Your Trophy Score is displayed on the top bar of the screen with a Trophy Icon. This is your overall Multiplayer score which can increase or decrease depending on your performance in an Event. When an event ends, your trophy score will be updated to reflect the overall points gained or lost in that event.
Your Event Score is the number of points earned in the Event itself. This affects who you are matched up against in the Event. The Event score also determines your ranking in the event and can be viewed at any time on the leaderboard.
Both Trophy score and Event score are considered when determining how many points you receive for beating other opponents. For example; if your score is significantly higher than your opponent then likely you will earn less points because the opponent will be likely to have a worse hand and be easier to beat.