A childhood belief about family

Until I was about four years old, I believed that my older half-sister was actually my cousin. We shared the same father, but she lived with her mother several states away. All but one of my cousins at the time were older than me (none the same age), and we only saw them once every few months (or even years), the same frequency that we saw her. When she came for a visit that year, I said something about her being my cousin. My mother looks at me strange and goes, "No, sweetie, she's your sister." This confused me, because all of my little friends lived with their siblings in the same house, but my sister lived far away. My mother explained it to me, but I didn't become totally un-confused until it hit me later until the concept of divorce was explained further.