Milchig is the Yiddish word for dairy. And the German word for milk is milch. Yiddish is a West Germanic language hence the almost similar word for dairy.
Anything that has milk in it, like cheese or cream, is dairy or milchig.
Milk actually comes from meat. Say what? Yes, the milk we drink and the milk-based foods we eat, like ice-cream, comes from animals that are 100 percent meat. Like cows, and goats.
Sounds like a contradiction. How can something that is produced in a pure meat entity bring forth its opposite? In a similar scenario you have a male baby developing for months and eventually exiting from a female body.
(It’s interesting to note that human milk is parve. So, if there was a medical requirement for an adult to drink human milk, he could have a cup of it with his hamburger.)
There’s a lesson to be learned from the fact that something can produce its opposite – like a male from a womb and milk from an animal. In a similar vein, an evil person can have saintly children and a tzaddik can have evil children. The lesson to absorb: judge what’s in front of you, not where he/she came from.