A higher quality intelligence than us might, among other things, use better heuristics and more difficult analytical concepts than we can, recognize more complex relationships than we can, evaluate its expected utility in a more consistent and unbiased manner than we can, envision more deeply nested plans and contingencies than we can, possess more control over the manner in which it thinks than we can, and so on.

A more general intelligence than us might simply have more hardware dedicated to general computation, regardless of what it does with that general ability.

In practice for "quality" we normally have a yardstick for performance which is being improved continuously (e.g. success probability, quality of a solution to an optimization problem, ability to win in a game), while for generality there is often no such yardstick. At best this seems like a difference of degrees rather than a difference in kind though.

I don't know if there is some more convincing distinction. I can't think of any arguments that depend on a distinction.

Perhaps a more general intelligence can do well in a wider variety of circumstances, whereas a higher quality intelligence can do better in those circumstances, by seeing better solutions etc rather than just being faster.

Intelligence is the ability to achieve complex goals in complex environments.

The greater the total complexity of the set of goals that the organism can achieve, the more intelligent it is.

Goertzel 2006, p43

Bostrum unsatisfactorily defines quality superintelligence in a self referencing circle by vastly qualitatively smarter (p56). It would have been better to name the ability to solve problems of vastly higher complexity.

Intelligence of higher generality covers more domains.

You can improve in intelligence by generalizing ('My intelligence improved in generality'), or by further investing in what you're good at ('My intelligence improved without improving in generality'). It seems like we could mean two different things by 'generalizing'.

Suppose four skills exist, A,B,C,D; and my skill level can either be low (0), mediocre (1), high (2), or very high (3). If I start off with A=0, B=1, C=2, D=2, then 'generalizing' might mean improving A or B more than I improve C or D. Alternatively, 'generalizing' might mean improving in more skills, rather than in just one. On the former conception, 'raise A to 2' increases my intelligence's generality more than 'raise C to 3 and D to 3'; on the latter conception, the reverse is true. There's plug-the-gaps generalization, where you try to get rid of your weak points; but there's also spread-the-love generalization, where you try to find self-improvements that will impact your problem-solving ability in as diverse a range of problems as possible.

'Qualitative intelligence improvements' seems like a grab-bag for 'all the kinds of intelligence improvements that we don't usually measure in any simple and direct way'. We routinely talk about, e.g., the speed, number, and computing power of computers, in terms of simple numerical values; we don't routinely do the same for computers' language-processing abilities, so that goes in the 'qualitative' bag, at least for the moment. Improving in qualitative intelligence could take almost any form; it seems like a less natural category than 'generality'.