Those are big smarty pants words for "means vs ends".
Consequentialism (also utilitarianism) says the ends justify the means. What's moral is determined by the "greatest good for all". Deontology says ethics are formulaic, logical, and based on universal rules or principles. A deontologist could say it's "okay to lie sometimes", but only if they can define "sometimes" rigidly e.g. to do no harm.
Consequentialism is for the intellectually lazy, making up the rules as you go. I find that most statists gravitate towards utilitarian arguments. They love factoids. When you press them for consistent ethics, they get uncomfortable (see cognitive dissonance). I find individualists sincerely enjoy deontological ethical discussions, yet we seem far outnumbered in the world. That said, many individualists hold their own with utilitarian arguments (e.g. Ludwig Von Mises, Milton Friedman). Nobody wins such arguments since factoids are contagious and plentiful.
Political debate often seems to be about who wins the "moral highground". A good example is "taking from the rich to help the poor", which is a utilitarian position. The utilitarian will claim it's a consistent ethical position until you challenge them "What about us helping Africa or India?". They will retreat, unable to rationally define their ethical rule why they don't give away their money - grasping for something like "we can't help everyone", "americans should help themselves first", etc. Moral highground lost.
I would challenge people to introspect and challenge the consistency of their own ethical positions. When debating politics, individualists can take the moral highground from statists by anchoring the conversation on universal rules and principles. Substitute factoids and mainstream assumptions with a priori models. A good mental exercise: If Person-A pays Person-B $1000 to attack you, who commits more wrong? Why? What if Person-B just attacked you to steal $1000 from your wallet? What's the difference?
On that note - I link to Jan Helfeld
A quirky guy who interviews politicians with deontological questions... leading to hilarity and hypocrisy on a few occasions.