The Giro, before this year, didn't award cat.4 at all, only 1-3, and many tough climbs weren't categorised at all. Plus, all mountaintop finishes used to pay the same number of points as a cat.1 climb does now (which is more than a cat.1 climb used to). This meant that the GC contenders would always be close to the maglia verde, so a rider would either need some big points-accumulating performances (Pérez Cuapio 2002, Piepoli 2007), to be a GC contender themselves (Garzelli 2009), to be a rider who dominated the category by being GC capable and targeting the jersey to the point of making competing for it pointless for all others (Rujano 2005, Sella 2008), or to go in an insane number of breakaways to accumulate the small points (Wegmann 2004, Lloyd 2010). The MTF category also meant that short climbs, such as Pescocostanzo in 2008 or San Luca in 2009, would give more points than legit hors catégorie climbs.
This year, the old system would have had Macugnaga and Montevergine di Mercigliano offering more points than Crostis, Finestre or Fedaia, which is why they've shuffled it a bit.
Cima Coppi = Cima Coppi
Old Giro MTF category = New Giro cat.1
Old Giro cat.1 = New Giro cat.2
Old Giro cat.2 = New Giro cat.3
Old Giro cat.3 = New Giro cat.4.