You can view your score for playing a song in the song summary screen. As an example on the screen below you can see that
- 33900 is the previous highest score for the song;
- 40600 is the new high score for the latest performance of this song (all parts).
The number shown on the Leaderboards (41400 in this case) is a combined score - the sum of the best scores achieved for all parts of the song during previous plays.
Once the song is relaunched, the new High Score of 41400 will replace the previous value of 33900