I have seen people mention "Optimized Clients" in several places, but have not been able to find a good explanation of what this means.
Would anyone care to explain?

An optimized client doesn't do much. By Client it's meant the BOINC daemon.
Sure you can optimize BOINC, but why do so? BOINC is a managing program, it doesn't crunch much by itself.

Some 3rd party people have released Optimized BOINC versions that allow you to set your benchmarks by hand. That way you can claim lots of credit on certain projects. Some projects even give you that credit then.

The other thing that's being done though is on those projects that have their science application in Open Source. By using a different compiler than Berkeley uses, you can compile for instance the Seti application to use SSE and SSE2 instructions. Results crunched with these applications crunch faster, while still claiming the same credit.

Although even then it can be tweaked, so the application can ask .5 to 3 times as much credit.

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The risk with optimised science apps is that they don't return the same results as the original version. We've just spent several months trying out several different optimisations for the climate model (various levels of SSE2 on a million line Fortran app) - every single SSE2 optimisation gave results which didn't match the current version. The SSE2 did give around 5% extra speed, so it would have been good if it had worked.

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Do not confuse optimized client with optimized science application. An optimized science app crunches faster, giving more useful results per minute back to the project. An optimized core client gives you more credits (sometimes) but not being useful, so it could be called "cheating"!

The risk with optimised science apps is that they don't return the same results as the original version.

Why is it different? I don't know much about SSE, but I might guess that it doesn't have the 80-bit intermediate results that "doubles" normally do?

Optimisation (in it's most basic form) is rearranging the order of calculations in order to make them quicker. In more sophisticated forms (SSE2 etc) its changing the operations to different ones which run quicker.

Even the simple optimisation of reordering calculations can change the precision of the result - for example, if you do a multiply first (> 1), then add, the result is to a higher precision than if you add first them multiply.

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