Why is Passiontide before Palm Sunday when Christmastide and Eastertide are after their feasts?

I've been a Catholic my whole life and this Lent is the first time I've ever heard the term Passiontide. I was just wondering though, because it doesn't seem to fit the same trend as the other mini-seasons, why does it start the last two weeks in Lent and isn't simply synonymous with Holy Week? And if Palm Sunday is Passion Sunday, why would Passiontide start before it?