The traditional nuclear family model consists of a married, heterosexual couple living together with their own biological children. This was the model for how an American family was “supposed to” be for a long time. Today, many other models have come into use.
One such model is the blended family. This comes about when divorced people remarry. If one or both of them have children from their previous marriage, they end up in a situation where they have stepparents and stepchildren and stepsiblings. There may eventually come to be half-siblings as well.
Another model is the single parent. This is becoming more prevalent today, particularly among lower-income people. In these families, the parents never marry or they divorce and have yet to remarry.
A much less common model is the extended family. This is when there are relatives like aunts and uncles or grandparents living along with a family. This is not very common today but can be found among immigrants and in families where adult children need to care for aging parents.
Finally, there is the same-sex couple. I would not call homosexuality a “lifestyle” but the decision to form a same-sex family with children is a lifestyle choice. This is, of course, still controversial in many places, but it is becoming more common as attitudes towards homosexuality become less rigid.