In the relationship between a mother and daughter, mothers also generally use typical "feminine" things to bond with their daughters as well, shopping trips and dance classes for example. One thing I feel is also common in a mother-daughter relationship is that between the mom and the dad, the mom is more likely to punish the daughter than the dad is. Generally I feel like a mom is less naive, not as caught up in "daddy's little girl" ideas, and more suspicious of what her daughter is doing. In my opinion, this is caused by moms remembering all of the things they hid from their parents when they were their daughters age, creating cause for worry.
The relationship between a mother and a son is generally much different than a mother and a daughter. From my experience, a son can get away with a lot more than a daughter can, when it comes to a mom. As a personal example, my older brother never had a curfew while in high school, while my sister and I, on the other hand, had very strict curfews up until our 18th birthdays.
I think that the most common type of relationship between a father and his daughter includes the idea that she will always be "daddy's little girl". This begins at birth and goes through her first date, prom night, and even wedding day. A lot of dads have trouble being as strict to their daughter as a mom would be, unless it is on the topic of dating. I would be surprised if I met a father who was thrilled to meet his daughter's first boyfriend, so I feel that this is common in most father-daughter relationships.