Specialists sometimes like to talk as if post-secondary funding is some kind of arcane science.  But if you cut to the chase, it’s actually pretty simple.  You can tinker around the edges, and you can use different techniques to fund different parts of the system, but fundamentally there are only these five approaches:

1. Subsidize nothing.  Some education is private and does not attract any subsidy.  In fact, in large swathes of Asia, Africa and Latin America (not to mention about a quarter of the US system), universities run simply on what the market will bear.  Even in countries where undergraduate education is subsidized and available at publicly–funded universities, some parts of the system may still run on this principle (e.g. executive education).
2. Subsidize everything.  Some education, on the other hand, is completely subsidized.  Much of Europe works on this principle, though it is an international outlier.
3. Subsidize differentially based on merit. This is pretty simple: take some kind of examination or, less frequently, a multi-dimensional body of academic achievement, look at the comparative results, and subsidize the ones you think are most meritorious.  In lots of countries – mainly but not exclusively ex-socialist ones – this is the way funding is handled: free tuition for “the best”, everyone else pays cash (and yes, that’s every bit as regressive as you think it is).
4. Subsidize differentially based on family income.Essentially, poor students get a greater subsidy than rich students.  That’s the principle which underlies most need-based student assistance systems, and certain types of targeted free tuition programs, such as the ones in Chile and Italy.  I have previously argued that this makes a whole lot of sense given that low-income families over-estimate post-secondary costs and under-estimate post-secondary benefits; targeting grants to these people levels the playing field in terms of perceptions of return on investment (this matters if you think Human Capital Theory matters, but less so if you don’t).
5. Subsidize differentially based on future student income.  This is a bit trickier, but it’s at the heart of at least some income-contingent loan schemes.  This approach posits that student repayments should bear at least some relationship with the private return on investment.  So, you can subsidize differentially by charging different amounts to programs based on expected private returns (e.g. more for law and dentistry, less for Arts), which is what Australia does and to an extent what happens in Ontario.  Or you can charge everyone high fees, and massively forgive loans in 15 or 20 or 30 years if it turns out the student has low returns.  In principle, this latter approach (most notably used in England) is exquisitely rational because it discriminates minutely between individuals based on actual returns over a period of decades.  The problem is it depends on people not freaking out about having a huge nominal debt in their name their entire lives.

Honestly, that’s it.  At the margin there’s a little bit of discussion about how best to handle the bit that isn’t subsidized (how much of it gets dealt with by loans and if so, what kind of loans), but in the grand scheme of things, that’s kind of small potatoes.

What national/provincial/state policy makers do for the most part is to combine these policies in different ways.   Public funding to institutions is subsidy category number two: nearly all government do this to some extent (though not for all institutions, or programs of study and not all to the same extent).  In North America, category 3 is much less common than category 4, though it certainly exists (most notably in state merit aid programs like Georgia’s HOPE scholarships).  Category 5 didn’t exist at all twenty years ago and still doesn’t for the most part in Canada, though various US income-based repayment plans with generous forgiveness policies are starting to change this.  England is dead set on using category 5 to charge for tuition, but until recently used category 4 to determine access to support for living expenses (i.e. maintenance grants).

Because most governments use a combination of policies, big policy questions can often be thought of in terms of how they shift the boundaries between different subsidy types.  When a government decides to cut funding and raise tuition, it is changing the boundary between the subsidy category two and all the others.  When a government de-regulates fees for international students, it simply means it is taking a particular category of students and placing them into subsidy category one.

Not quite all policy can be described this way: for example, an increase in operating grants, in the absence of change in fee policy, does not change the boundaries between policies, it just means one policy is being funded more intensively.  But when comparing different national policies, I find this approach to be quite helpful in thinking about how governments choose to spend their money.