Last question first.
No, a polar covalent bond is not the same as a covalent bond. A pure covalent bond occurs between two atoms of the same kind; for example, H2, N2, Cl2, F2, etc. But if the bond is between two different atoms what might otherwise be a covalent bond is a polar covalent bond. HCl gas is a polar covalent bond because H has an electronegativity of 2.1 and Cl has EN of 3.0 (check me on that--this is from memory). HF is polar covalent as is HI, HBr, etc. ClF is polar covalent. It is true that all polar covalent bonds are covalent but not all covalent bonds are polar.
Now to the other part of the question. You're right, the difference in electronegativity is the way to know if the bond is covalent, ionic, etc. Where is the dividing line? About 1.9. Some books use 1.7, some have used 2.0 and different teachers use different cut offs. I was taught to use 1.9 as the 50-50 mark; that is, a difference of 1.9 meant the bond was 50% covalent/50% ionic. Few bonds are 100% ionic and few are 100% covalent. GENERALLY, we call the bond ionic if it has more than 50% ionic character and we call it covalent if the bond is more than 50% covalent character. An EN difference of about 1.0 is 25% ionic/75% covalent. Technically those are polar covalent bonds although we may refer to them as covalent. NaF then is ionic with an EN difference of 3.1. I call NaN3 ionic; the EN difference is 2.1 but it may be about 60% ionic/40% covalent or something like that.
I hope this helps clear up the confusion.