this might be a dumb butter question
Yes, melted butter is just that, butterfat, water, and milk solids, approximately 80% butterfat, 17-19 % water, and 1-3% milk solids
Clarified butter is only butterfat, 100%
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It is normal butter, heated until it break, and the milk parts foam. Take off heat. If you pour it in a clear container, you will see that it separates into three parts basically: Milky liquids on the bottom, the clarified utter, and any film on top is just what "impurities/solids" have cooked and stayed up top. Skim the top, and pour/ladle out the middle section for clarified butter(BUTTER containing non of the milk solids).
All you are doing, is removing the milk solids, it's no big deal.
Leaving butter "whole", like for a burre blanc, is simply mixing in the butter to a base sauce/sweated aromatics, and adding whole butter, while whisking constantly, so the butter does NOT break, and so the butter remains whole, and stays as a "sauce".
If you reduce butter down, no frills, you end up with Browned Butter, a great addition in it's self, especially for cauliflower, rainbow trout/fresh water fish, pasta/ especially gnocchi. Or, when making caramel for sauce, it adds some earthiness to it that pairs well with coffee, dark chocolate, and even (other end of the spectrum)pralines and desserts like Paris Brest.
You reduce it down FURTHER. . . .you end up with burn butter, good for nothing more than making the house smell pretty good for a bit.
~If you are what you eat, I am cheap, fast, and easy.