Why is an ionic bond a chemical and not a physical bond? Ionic bonds seem to be intermolecular but are classified as chemical bonds.

&quot;Ionic bonding is a type of chemical bond that involves the electrostatic attraction between oppositely charged ions.&quot; -  Wikipedia, definition of an ionic bond
&quot;The physical force of attraction which holds atoms and molecules in a matter is called a physical bond. van der Waals' forces and coulombic forces are physical forces.&quot; - Chemistry Stack Exchange, definition of an intermolecular force
&quot;A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electrostatic force of attraction between opposite charges, either between electrons and nuclei or as the result of a dipole attraction.&quot; - Wikipedia, definition of a chemical bond

Before an ionic bond is formed, oxidation and reduction must occur. For example, let's use sodium chloride. A chlorine atom will steal the outer electron from a sodium atom. The chlorine is gaining an electron, i.e. being reduced. The sodium is losing an electron, i.e. being oxidized. I agree that this is a purely chemical process.
Now that the atoms are oppositely-charged ions, they can attract and form an ionic bond:
$$\ce{Na+ + Cl- -&gt; NaCl}$$
My question is this: How is this bond defined as a chemical bond?
Let's take water; $\ce{H2O}$. The oxygen forms two polar-covalent bonds with two hydrogen atoms. Each hydrogen shares two electrons with the oxygen. The electrons are being shared, so this bond an intermolecular force. The atoms stay together because they both depend on the electrons they share.
Now let's take more than one water molecule. These molecules will form hydrogen bonds. The hydrogens on the water molecules do not often have an electron around them because the oxygen has a greater attraction with them. This leaves the lonely proton of the hydrogen to make that end of the water positive while the oxygen is negative with its electrons. The negative end of the water (oxygen) will become attracted to the positive end of another water molecule (hydrogen), forming our anticipated intermolecular force. Does this sound familiar?
I hope it does. According to my knowledge, an ionic bond is that, but instead of a dipole-dipole interaction, it's a monopole-monopole interaction. If you look at the bond itself and not the reaction forming it, it acts just like an intermolecular force.
Short version:

We don't call bonds "physical", there are chemical bonds and other types of interactions between particles. The chemical bonds are classified this way because they make up molecules, salts, polymers and such, which are the materials chemists are interested in studying, and not particularly because of their sub-atomic/electrostatic characteristcs. 



Your question relates to two frequent sources of confusion: 


How do we define a chemical bond? What makes a bond between two atoms ionic or covalent?
Where does chemistry (hence chemical interactions) ends, and consequentially where does physics (and hence physical interactions) begins?


Both questions have been pretty much answered here on Chemistry SE and also on Physics SE. I'll give some links to related questions and also a shrot summary.

1. How do we define a chemical bond? What makes a bond between two atoms ionic or covalent?

Your question didn't go much into covalent bonds, but anyone trying to understand anything past the surfaces of chemical bonds should know that the definition of a bond as covalent or ionic is simply an easier way for us to classify things, because when the bonds are categorized in groups we can say that one group behaves in a way, and the other behaves in a different way. The truth is, all bonds have some ionic and some covalent character to them. 

Good answers here on Chemistry SE about that can be found here: 


Can 100% covalent bonds exist?
What happens if the electronegativity difference is exactly 2.1?


2. Where does chemistry (hence chemical interactions) ends, and consequentially where does physics (and hence physical interactions) begins?

For a Physics pont of view, see: What distinguishes between physics and chemistry?

For a Chemistry point of view, see: Differences between chemical physics and physical chemistry?

Basically, it's clear that both sciences have a lot of overlapping, and perhaps the main difference is the approach taken and how the results will be used. While chemists usually focuses on understanding the structure and interactions between substances and materials, in order to be able to improve them or develop new ones, physicists are mostly interested in understanding the exact laws of nature and representing them with mathematical equations that can be used to explain and predict phenomena. This definitions do not seem so different, and that's not supposed to be wrong: We do have the Physical Chemistry and Chemical Physics fields.

Ok, but Why is an ionic bond a chemical and not a physical bond?

Two important things were mentioned by @Mithoron in the comments. The term "Physical bond" is not frequently used by chemists, (or anyone I suppose), pretty much because all interactions in whole universe are physical. This single quote by @Mithoron is related to the two points I highlighted above. Both "types" bonds "follow" the same laws, and there is no hard line between them.

It's also worth noting that the definition you gave for Physical Bond was taken from an answer without a single upvote, which is an indicator that it isn't what the Chemistry SE community thinks (despite the fact that Google liked it very much and uses it in it's short-answer for the query). Another indicator that "Physical Bond" isn't really a type of bond is that there aren't definitions of it out there (Yahoo answers doesn't count), not even a Wikipedia article.

So why do we call them chemical bonds? 

That's pretty much because the bonds we call chemical are those which make up molecules, salts and other materials which are mainly studied by chemistry. The definition of chemical bond varies a lot (as explained here), but they are the bonds which create what chemists study. 

Other types of bonds which aren't called chemical are the intermolecular interactions, which are obviously of interest to chemistry, but also the Strong Force, which is the force that binds protons and neutrons (nucleons) together to form the nucleus of an atom. (I hope it's okay to call Strong Force a bond, I'm not sure to be honest).