Generally, squishy champions are often refereed to range champions. They can attack enemy from distance, and so, they usually only build damage on them.
On the other hand, melee champions need to be very close to enemy to do damage. During team fight, they are the most easy one to target. So, they usually build some defense items to increase their survivability. Some even have skills to increase their defense. These champions are often refereed as bruisers or tanks.
As for the difference in stats, I think Devious explains it all