I'm learning about electronegativity in atoms and how their difference affects the type of bond they make. I know that no difference makes a non-polar covalent bond, a difference less than 2.1 is a polar covalent bond, and a difference above 2.1 is an ionic bond. But what kind of bond forms if the difference is exactly 2.1?
As mentioned above there is no hard line between an ionic and a covalent bond, they are just two ends of a spectrum where a bond can have a certain degree of ionic or covalent character. At the lower end of this spectrum, bonds with small electronegativity differences between the atoms have very little ionic character because the charge distribution in the bond is almost symmetrical between the two atoms. As the EN difference increases the charge distribution becomes asymmetrical and this results in an increasingly polarised bond, which therefore has an increasing degree of ionic character. Eventually at the other end of the scale you have a bond where almost all of the charge is concentrated on one atom and this is generally termed to be an ionic bond.
So in answer to your question; what happens if the EN difference is exacly 2.1; nothing happens, you have a relatively strongly polarised bond which under some definitions might be classed as ionic and under others as strongly polar covalent but in reality it has a large degree of both ionic and covalent character.
Based on the the answer to this question:
Here is a very nice graph of percent ionic character as function of electronegativity difference for some common binary compounds. Here ionic character can be thought of as the degree of charge separation across the covalent bond. Compounds with 50% or more ionic character are considered "ionic". This division of classes of compounds is arbitrary.
Image source: University of Florida Chemical Bonding page