From a GEDCOM point of view and therefore many programs, a FAMily is a record that connects male and female "spouses" with children. While marriage is a TAG/Field in the record it is NOT required.
Children can be attached to the FAMily record via a FAMC tag associated with the INDIvidual and a subtag called PEDIgree that can denote the child is a (adopted | birth | foster | sealing) connection to the FAMily. NOTE: FTM does not support this specific GEDCOM construct but does track the information. (EDIT: The FAMily is also attached to the INDIviduals as well, The connection is bi-directional.)
Spouses of a family are connected to the FAMily record via a FAMS tag.
So FAMily and Marriage are connected and could be the same but individuals are connected to a FAMily record without the requirement of marriage so depending on how the counts are made they could be the same or different.
In GEDCOM a Male and/or Female "spouse" is not required to "head" a family. And while the GEDCOM allows for only one of each (male and female) this is not a requirement of many software programs, nor is it a requirement that anything except one person (be it spouse or child) be associated with a FAMily record. So it is possible to have a child without parents, or parent(s) without children, or child(ren) without parents.
Personally I have a few "spouses" without children, "spouses" without marriage (with and without children), cand cases where children have no know parents.
Many software programs tend to LUMP concepts together because it gets real hard to differentiate between the concepts "in the wild". Some people call themselves "married" but no documents are on the books. If you frequent genealogy blogs you will see many discussions about what constitues a family, what is a "common law marriage", how to record various family (and non family) relationships. Some people only record true blood relationships, other only record the male or female lines, other do something very different.
Sorry for the long winded answer. Your titled question is not easy to answer with the bigger picture in mind.