It's relative to the speed changing feature.
To use that feature, the client first needs to make a full run on the replay, which sometimes takes a bit of time, specially if you're trying to open big replays.
When you press normal load, the client runs the replay once before showing it to you, enabling the speed changing feature as soon as the replay is presented to you.
When you press Quick load on the other hand, you are telling the game that you don't need to use the speed changing feature, so the game doesn't need to run the replay once secretly before showing it to you. That's why the replay loads faster.
Did that clear your doubts?