You are correct.
Someone who is asymptomatic is infected with the virus but not have any symptoms of the disease. But there is also a window between when you become infected and when you do have symptoms. This is the incubation period. You could still be infectious and shedding the virus even though you do not have any symptoms. This is the real danger here. Scientists are beginning to think that, yes, whether or not you have symptoms could relate to genetics. Could be genetics of the viral particle that infects you. Not all SAR-CoV-2 virions are the same. A small genetic change in the virus could make it more or less pathogenic. Or, your own genetics could play a role. You could have a small genetic change in the receptor that the virion needs to infect your cells; that change could lessen the ability of the virion to enter your cells. Or, you could have a change in proteins involved in your immune system that allows you to fight off the infection better or worse than someone else.
As yet there is no evidence of in-utero transmission of the virus yet. Infection does not appear to cause any developmental problems in fetuses; it is not like infection with the Zika virus.