Opinion of relationships, depicted in this illustration... hmmm.
First of all, in my opinion, terms "lovers", "members of the same family" and "friends" aren't mutually exclusive. I perseive them more like different dimensions of one big space of interactions and feelings, which are called "relationships between two people".
For example, some people are friends with their family members, some aren't. Lovers also can be friends or not. Family members can be lovers or not, too. And of course, friendship, love/sexual attraction and family feelings can be presented in the same relationships altogether.
If I don't understand particular type of relationship between people (or between me and another person), but see that they're kind to each other and feel interest and respect to each other's personality, I say that they're friends by default. Because in this case, friendship is presented clearly, while other aspects aren't clear, so I call their relationships by that aspect, which is the most clear for me (but without excluding other possibilities, of course).