'Family' would be one thing. I found that 1) the responsibilities/rights were much broader, and 2) they extended beyond just siblings, parents (and perhaps grandparents).
If one of my siblings were to have financial trouble, or to start a business, it wouldn't be strange for me to decline helping them, whereas in the more traditional culture this would be considered rather selfish. And on the latter culture, when your parents get older and less useful to society, they move in with one of their kids (and often help out with the child-rearing). Putting them in a home would be unacceptable.
Furthermore, many of these things would extend to uncles and aunts and cousins, where in my current culture it's pretty normal to only see those at 'special' family occasions.
I also found that the relationship with neighbors and small businesses in the area were a lot more 'familial' in nature: 'watching the shop while owner does x', the shop-owner getting particular products just for you, but also a sense of loyalty. If you need a haircut/pedicure/etc., and a family member offers that service, it would be considered offensive to go to another place.
Basically, a lot of the stuff that 'we' would put in the transactional sphere were often much more like how we'd interact or deal with immediate family. A lot consisted of favors you'd do, with the implicit agreement that someone should do something equivalent for you. These intricate 'networks' of favors combined with various social obligations led to ties that were much stronger, obviously, than a purely commercial interaction.
I'm rambling a bit; still early here. I suppose a good book on the matter is Debt by David Graeber, but looking at how various immigrant communities operate can also be enlightening. I've experienced similar kinds of quasi-commercial relationships with the Turkish shops in my neighborhood, for example (I would fix their computer, they'd hold on to my house key for a friend to pick up, no shopping without chatting, etc.).