What is the difference between ionic compounds and covalently bonded compounds?
In general, ionic compounds occur when a metal ion and a nonmetal ion make a compound. When they are a compound, electron(s) are transferred. Ionic compounds will generally conduct electricity as a solution, are brittle, hard, and tend to have high melting and boiling points.
Covalently bonded compounds are generally nonmetal atoms that become a compound, and when they are a compound, they share electron(s). Covalent compounds have low melting points and are poor conductors of electricity (however, an example of something that defies this description is graphite, which is a carbon allotrope that conducts electricity due to electron delocalization).
It is erroneous to say that metal/nonmetal bonds are always ionic, in fact, there are no 100% ionic bonds. Bonding lies along a continuum between 100% covalent and bonds which have a high percent ionic character, but even those have some covalent character as well.
You are better off distinguishing between compounds which exist as networks or lattices and compounds which exist as discrete molecules. Compounds which exist as networks include salts with highly polar bonds, like NaCl, and compounds with high covalent character, like SiO2. These are the ones with high melting points. Diamond and quartz have very high melting points and are very hard and both have very covalent bonds.
Statements like the one above are vast oversimplifications riddled with misconceptions.