The key point is that these names don't describe the physical speed of the train, but rather the service category — mainly how many stations the train skips.
特急 (limited express) skips the most stations, so even if its top speed is similar to other trains, it reaches the destination faster.
急行 (express) skips fewer stations than 特急, and 快速 (rapid) stops at even more stations.
So "faster" here means faster overall travel time, not necessarily a higher maximum speed.
Historically, the names were given step by step as new services were introduced, so the wording may feel counter-intuitive if you look at the kanji meanings alone.