A 'matriarch' is a woman who holds a lot of power or influence in a family or organisation, and generally spans beyond the boundaries of a single household. A 'head of a household' holds the most power and influence in the household, and does not necessary expand beyond the household. 'My mom is the head of my household.' <- the mom has the final say in things regarding her household. 'My mom is the matriarch of my household.' <- this sentence means the same as the one above, however its usage here seems unnecessary unless there is another contending strong female influence living in the same household (aka grandmother). 'My mom is the matriarch of the family' <- meaning your mum has the most influence in the family, even over the men and other women. I hope this helped you out.

A mom = Your mother whether natural/biological or adopted or a women who has taken on that role. Or even a women you yourself consider as being or is your mom. A matriarch = Is an older powerful women. in charge of an household, or a tribe etc and whose power is passed down from mother to daughter. There are occasions when you mom can also be a matriarch. or a matriarch can also be or become your mother figure.