What's the difference between an ionic bond and a covalent bond?

They're both similar but form between different types of elements. An ionic bond will form between a metal and a non-metal. The metal will donate electrons and the non-metal will accept the electrons, forming a positive ion (from the metal atom) and a negative ion (from the non-metal atom). The two ions then stick together through electrostatic attraction, forming the bond.
A covalent bond typically forms between non-metals. Instead of donating and accepting electrons, the two atoms will share a pair of electrons (usually one electron from each atom). The bond is again an electrostatic attraction but this time, it's between the two nuclei (positively charged) and the shared pair of electrons (negatively charged). The force that forms the bonds is the same whether it is an ionic or covalent bond but the difference lies in the locations of the electrons.