I cannot speak for Klippel. Your question seems simple but the answer can get very complicated because there are so many factors and variables beneath it.
Measurements often require multiple sweeps to obtain a reasonable average result and that will reduce noise. AFAIK, Klippel is focused on measuring loudspeakers, so they are probably pretty insensitive to noise but want enough power (and low enough output impedance, which tends to go with higher-power amplifiers) to drive "any" speaker without having to worry about how much the amplifier is contributing to the measurements. I'd also want an amplifier in a test system to be very robust to test errors like accidentally shorting the output when moving a speaker or pulling a wire off (open the output) when testing. Since speaker distortion is typically orders of magnitude (factors of ten) larger than amplifier distortion, having super-low amplifier distortion is probably not a big deal. That is also true in the home, of course, but chances are you are listening at lower levels than when testing a speaker. You want the test tones to be high enough to be well above any background noise; ideally you'd test in an anechoic (very quiet) chamber, but the Kipple system is designed to not require an anechoic chamber, and that means more noise in the room. Which means more power from the amplifier to rise above the noise.
Back to your question, there does not have to be a difference, and there is often a lot of overlap since a good amp is a good amp. Good performance matters for both applications, but which parts of the performance matter to you may be different than what matters in a test system. But you may weigh things (parameters) differently for a home system. If the amplifier is in the same room you might not want fans. You are probably driving a single set of speakers and can select the amp for those speakers instead of an amp to drive all speakers. If you have highly sensitive speakers like horns you may want less power and higher SNR (lower noise floor). If your speakers are not very sensitive, you sit fairly far away, and the speakers have low impedance and high phase angles (they are hard to drive), then you may want a higher-powered amplifier that can handle low-impedance loads. There are also aesthetics (looks); a home amplifier is often exposed in a console or on a shelf and you want it to look nice, or at least fit in with the rest of the components, while a test system amplifier is often in a rack with other test equipment and looks do not matter. You probably want basic circuit and speaker protection in a home amp, but hopefully do not need the more sophisticated and tolerant protection a measurement (or pro) amp needs to survive repeated test failures (or mistakes), and may not need the cooling (thermal management and protection) of an amp designed to be used on stage or in a test system running at high power all the time.
Many other factors, but those are some quick thoughts.
So, many words to say "maybe, it depends"... - Don
