Family number is more likely to tell you about a specific group of people living together.
A 'dwelling unit' was defined by the census as a stand-alone house or a house separated from other houses in a block by walls. The family unit is defined as a group of people provided for in common. In 1870 the instructions specify that if a group of people share a common table, they are to be counted as a family.
Someone who lives in a basement apartment, granny flat, or whatever you call it where you live is in the same dwelling unit, but a different family. These types of houses often don't have separate addresses or apartment #s for the different units. But the people living in them might not be related in any way.
You could also consider, for example, two immigrant families or single mothers that share a single house or apartment to save money, but live as separate families (their finances are not mingled, they prepare meals separately, etc.). In older censuses, these would be a single dwelling unit, but two families. In 1950, they got rid of family # and it's just "House & apartment #" and "Dwelling unit." Now, they count everyone together and aren't collecting data or information on families that share.
I use family # in my written citations (when it exists). But my goal with a citation is to tell someone else exactly where they can find the record and the part of it I was looking at. I'm not trying to interpret the record for someone with the citation or convey all the information it contains.
