Usually when you make homemade butter, and sometimes some commercial semi-artisan butters, for example french Isigny Ste-Mère Unpasteurised, the butter has a, what I would call "creamy" texture. I realized its not what others consider creamy, but I lack a better word at the moment. Think ice-cream creamy not face-cream creamy. Seems almost like very thick cream (but also not talking about the liquid homogenized stuff sold as cream in supermarkets, but real cream you get when you let milk from a cow you just milked yourself stand and cream collects on the top). The butter has a kind-of ice-cream texture, but without the need to keep it cold, and you can cut it up with a knife and eat like pieces of some cheese and it feels tasty.
But most typical butters from the supermarket have none of that, and feel like a totally different product. Has a very oily texture, not much creaminess, and if you try to eat it like cheese it tastes almost disgusting, unpalatable. It seems more like semi-solid oil. Even higher quality butters like Irish Kerrygold which is touted as grass-fed, is very oily, actually its more oily then other commercial butters.
I also have the impression that the homemade creamy butter melts at a higher temperature then typical commercial butter, which would be already melting and not keeping its cube shape at a hot-day room temperature without aircon (~26-30°C, ~80-90°F) but the homemade butter would still stay pretty solid.
I am not talking about fake butters with vegetable oils added in, all of these butters are pure cow milk butters with 82% fat, nothing added.
What exactly in the process makes the difference in the result?
I don't think it's the pasteurization, as I've seen butter from unpasteurized milk which was also oily and not creamy, certainly much more oily then other butters I've seen. There seems to be a varying degree of oiliness vs. creaminess among various commercial and homemade butters, it's a spectrum, not a all-or-nothing thing. Some commercial butters feel less oily and more creamy then others.