In practical terms:

In my view, in most cases an offset account is the hands-down easiest way to make sure your money is always working for you, without having to think or manage it. 

It's a transaction account, directly linked to your loan account.  Whatever the positive balance is in your offset, it's automatically considered as netting off your loan balance when interest is calculated (typically daily).  You don't have to micromanage jam-jars and funds allocations decisions, it's all in one (offset) account.

If you prefer to directly overpay into your loan, then redraw back to loan available if and when required, you will have to pay a great deal of attention to what/when/how much/from where etc, to ensure your money is always working for you.  I'm an accountant and even I don't have the desire (let alone the time) to do that! 

Some people prefer the psychological difference of overpaying their loan rather than holding their funds in offset.  They feel like those overpaid funds are less available (though they could redraw them), and that the funds in offset are too readily available to spend.  If that's true for you then ok, but please remember to pay attention to how you manage your funds so that your money is always working for you.

In technical terms:

An Offset account can help you reduce the interest you pay on your loan.  By holding funds in this regular transaction account linked to your home loan, you are only charged interest on the 'net' balance of the offset and loan account.  So if your mortgage account is $500,000 owing and you hold $50,000 cash in your offset account, you'll only pay mortgage interest on $450,000.  You won't earn any interest on the $50,000.  You'd typically use an Offset if you're saving those funds for a specific purpose (eg new car, holiday, school fees, deposit on investment property etc), so don't want to pay down your loan permanently

On the other hand, a Redraw Facility is a right to pull back out (redraw) any excess payments you've made directly onto your home loan account.  Using the numbers from above example, your mortgage account balance would have been $500,000 but in chunks or over time you've overpaid $50,000 straight onto the loan balance to reduce it to $450,000.  So you'll be charged interest on $450,000. 

The net financial effect of the two concepts (offset & redraw) is the same- so long as you actively manage your overpayments in the redraw scenario.... which few people can consistently do. 

So what should you do?:

Of course there's more detail to understand and every person's scenario is different.  As always, I'm here to listen to your financial circumstances and goals and help you plan the best mortgage strategy for your needs, then find the best lender and mortgage as well.