For whatever reason most Americans use the word "customs" when they are, in fact, referring to immigration, when traveling internationally.
Customs as it existed a few decades ago barely exists in many/most countries today except pro-forma. You used to routinely get your bag searched. Now, with very few exceptions, you just walk through the green door. Part of it (of course, this may change) is that there used to be a lot of financial incentive to buying items abroad and importing in your luggage.
I have Global Entry but I don't think the US even has a customs form any longer.
Because entry is handled by CBP - Customs and Border Protection.
Immigration - which is the process of becoming a US permanent resident and/or citizen - is handled (mostly) by USCIS.
Other visas are handled by the State Department (foreign ministry).
Not an expert, but this is my understanding.