Covalent vs Ionic is an old, pre-quantum theory of chemistry. It's basically just
wrong, and would've been dead and buried along with contemporary ideas such as the http://en.wikipedia.org/wiki/Cubical_atom" , if it hadn't been for Linus Pauling (a big fan of cubical atoms, btw), who put a lot of effort into finding theoretical justifications for them from the then-new quantum theory. In retrospect, that effort was mostly political, getting chemists on-board with the new way of thinking. Nobody actually calculates the percentage of ionic-vs-covalent 'character' of a bond anymore, much less uses that number for anything.
Anyway, so if you're talking about covalent-vs-ionic today, you're talking about Pauling's theory. Now, in Pauling's theory, the ionic character can be calculated from the difference in (Pauling) electronegativities between the atoms. So to begin with, there's a sliding scale, and really no such thing as a purely ionic bond, nor any such thing as a purely covalent bond, except for a homonuclear diatomic, where the electronegativities are equal.
However: Pauling electronegativities are defined by the relative difference in homonuclear-diatomic binding energies of the two atoms! The end result is that the characterization of a bond between atoms A and B, in Pauling's theory, amounts to little more than a quantification of how differently elements A and B bind to each other compared to how they bind to themselves. That's why the theory isn't very useful; it doesn't amount to much more than a single-number quantification of how different the two elements are.
More http://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291097-461X%281999%2974:2%3C87::AID-QUA5%3E3.0.CO;2-E/abstract" , you can define a 'covalent state' and an 'ionic state' in Valence-Bond theory (Pauling again), and view the thing as a quantum-mechanical superposition of these, but not only is there no binary distinction then, but a bond can't be characterized in terms of two states alone either. E.g. many textbooks claim that VB theory fails at describing the triplet ground-state of O
2, probably because they tried to describe it in two wave functions, properly you need to take into account a three-electron-bond state. (The origin of this myth seems to be due to repetition of an offhand remark by Lennard-Jones.)
johng23 says:
We call a bond ionic when the electron density is concentrated more near one of the two atoms participating in the bond.
That's an
interpretation of "ionic character", and unfortunately one that's still commonly taught. I say 'unfortunately' because it's also wrong. You're basically explaining a vaguely-defined property in terms of another vaguely-defined property, because there simply isn't any clear definition or measure of what it would mean for a bonding electron to 'belong' to one atom more than another. There are various quantum-chemical methods of 'population analysis' to arrive at some kind of number for this (e.g. Mulliken populations, Löwdin populations), but one thing they all have in common is that they're pretty useless at describing chemistry. You can't even get a reliable measure of oxidation states from them. (
Spin density, on the other hand, does say a lot)
So in summary: Electronegativity represents something real, albeit vaguely defined. The
polarity of a bond is quite real, it's easily defined theoretically in terms of electrostatics and can be measured directly as the dipole moment. But things like orbitals, covalent-vs-ionic bonds and resonance structures are entirely theoretical constructs. And out of those, the concept of covalent/ionic is the one that's both least theoretically justified and least useful in describing reality. I'd suggest people just forget about covalent versus ionic, metals versus non-metals, etc, and just talk and think in terms of polarity (which is what most chemists do anyway). HCl has a dipole moment of about 1 D, NaCl has about 9 D, KCl about 10 D. But there's no real reason to consider them to have different bonds; in MO theory they're the same bonds, you just have different effective nuclear charges, and hence different polarity.
(I swear, if these covalent-vs-ionic questions keep popping up, I'm going to end up writing a whole article for
J Chem Ed 
)