Opinions on dice thresholds.

Im wondering if any of the rulebooks have a hard-line stance on this; but maybe someone could clarify something for me.

When you or a creature rolls to hit and the AC is lets say a 14. Does a 14 hit? Or do you need to roll a 15 to "beat" the AC value?

Likewise for spell save DC; if the save is 13, do you need to roll a 13 or a 14 to succeed?