I grew up in Detroit, and I would describe the typical zip sauce as being a lot more like this recipe:
Zip sauce
3 cups water
1/4 cup Maggi Liquid Seasoning
2 tablespoons beef base
1 teaspoon pressed garlic
In a saucepan over medium high heat, combine ingredients. Heat to a gentle boil for 1 minute. Strain. Use a 1 ounce ladleful of sauce on any grilled meat item.
I think the name is the regional thing. Lots of places around the country serve their meat in a similar sauce, which may be called "au jus." I think if you order a steak at many Greek diners around Chicago, it'll come swimming in something like this.