Look for "elliottbnewcombjr"For example, the thread titled "What SUT?...."
You asked, "why does a cartridge have a recommended load impedence from a phono stage and so many phono stages have adjustments for that?" Because each manufacturer wants his cartridge to perform at its best. So he selects a range of phono input resistances that ought to work well with his cartridge and publishes that information. The rule of thumb is that the input resistance of the phono stage should be not less than 10X the internal resistance of the cartridge (which is another published specification that you should be able to find easily). Most manufacturers do not stipulate one value; they usually will stipulate a minimum value which allows for higher values of input resistance to be used. The 10-fold rule is not cast in stone. You can get away with lesser ratios, but usually you don't want to go far below 10. The reason for this is that as the input resistance of the phono stage approaches the output resistance of the cartridge, more and more energy in the form of signal voltage is lost to ground. Also, the high frequency response starts to roll off. This whole issue mostly pertains to MC cartridges which are often run at phono input resistances much less than 47K ohms. For MM cartridges, you can forget about it and use the standard 47K ohms, to be found in nearly all MM phono stages.
You asked, "why does a cartridge have a recommended load impedence from a phono stage and so many phono stages have adjustments for that?" Because each manufacturer wants his cartridge to perform at its best. So he selects a range of phono input resistances that ought to work well with his cartridge and publishes that information. The rule of thumb is that the input resistance of the phono stage should be not less than 10X the internal resistance of the cartridge (which is another published specification that you should be able to find easily). Most manufacturers do not stipulate one value; they usually will stipulate a minimum value which allows for higher values of input resistance to be used. The 10-fold rule is not cast in stone. You can get away with lesser ratios, but usually you don't want to go far below 10. The reason for this is that as the input resistance of the phono stage approaches the output resistance of the cartridge, more and more energy in the form of signal voltage is lost to ground. Also, the high frequency response starts to roll off. This whole issue mostly pertains to MC cartridges which are often run at phono input resistances much less than 47K ohms. For MM cartridges, you can forget about it and use the standard 47K ohms, to be found in nearly all MM phono stages.