Lemons gave a great explanation on bond polarity, but I thought I'd throw in my two cents on ionic vs covalent bonds.
In ionic bonding one atom steals another atom's electron completely. e.g Na+ Cl- Now I don't believe that these two electrons are "sharing" electrons. They are just attracted to one another by their opposite charges like two opposite sides of a magnet. Cl has it's valence electrons filling an S orbital and a full P orbital now that it has aquired another electron thanks to it's high electron affinity (or z-effective). Na+ also has it's electron's on lockdown in a noble gas like configuration with full S and P orbitals.
In covalent bonding we're satisfying the octet rule without stealing... we're sharing! (awww😍) In a nonpolar bond like a diatomic molecule such as H-H the two atoms are sharing their electrons perfectly. There is no dipole moment (no place the electrons would rather be). They're happy being equally distributed because each proton has the same pull on each electron.
Now in a polar bond like C-O, the shared electrons will split time once again satisfying the positive charge of each atoms nucleus. However, the oxygen atom has a much higher electronegativity so you're gonna get some unequal sharing, but at least their still sharing... so it's not ionic bonding!
Quick summary: Sharing electrons=covalent which can be polar or nonpolar. Stealing electrons=ionic which are always uber polar.
One thing to consider is that while ionic bonds are polar they are usually broken apart in water. This results in a cation and an anion in aqueous solution.