Do ability tests predict maximal more than typical job performance?
The distinction between maximum and typical performance was originally established by Sackett et al. (1988), and since then, how to predict either and their relation to one another seems to have been a very active area of research. In fact, there is a prohibitively large literature on the matter for a full review.
Fortunately, your questions were recently addressed comprehensively, along with other inquiries about the relationship between typical and maximum performance, in the December 2007 issue of Human Performance. To start, one paper by Barnes and Morgeson (2007) which provides support for Ackerman and Beier's claim, in its descriptive sense, that typical performance is that which is of interest to employers, which found that compensation was predicted by typical performance and intra-individual performance variability, but not by maximum performance. I suspect the claim was made in a prescriptive sense, though, so let's continue and see where the evidence takes us.
In the same issue, Marcus et al. (2007) reported support for the long-standing claims that measures of cognitive ability, such as g, serve as predictors of maximum performance, whereas measures of personality serve as predictors of typical performance. Tables provided in this paper also suggest, to me, that a meaningful correlation between typical and maximum performance may be tricky or impossible to elicit, as does another paper in the same issue of the journal.
This paper, by Mangos et al. (2007), suggests that job performance in an ecologically valid setting tends to be characterized by a mixture of need for typical and maximum performance, which I think makes life somewhat difficult for Ackerman and Beier's claim about what IO psychologists and managers are interested in, in the prescriptive sense, with respect to performance. Methodologically, it is not clear how we ought to dissociate the two, and theoretically, it is not clear why we would want to.
In conclusion, based on this special issue on the matter, it seems the simplest answer to your question about ability tests and maximum performance is that ability test scores seem to account for a large amount of the observed variance. With respect to your question about the correlation between maximum and typical performance, it unfortunately appears the answer to your question is complex and not readily summarized.
References

Barnes, C. M., &amp; Morgeson, F. P. (2007). Typical performance, maximal performance, and performance variability: Expanding our understanding of how organizations value performance. Human Performance, 20(3), 259-274.
Mangos, P. M., Steele-Johnson, D., LaHuis, D., &amp; White III, E. D. (2007). A multiple-task measurement framework for assessing maximum-typical performance. Human Performance, 20(3), 241-258.
Marcus, B., Goffin, R. D., Johnston, N. G., &amp; Rothstein, M. G. (2007). Personality and cognitive ability as predictors of typical and maximum managerial performance. Human Performance, 20(3), 275-285.
Sackett, P. R., Zedeck, S., &amp; Fogli, L. (1988). Relations between measures of typical and maximum job performance. Journal of Applied Psychology, 73(3), 482.