亲生 = 养子养女 ！= 继子继女

stepchildren are just children of your spouse from a former marriage.  You have no legal relationship with them. 

If there is no weill, step children  don't inherit the deceased's personal property. Adopted children are the same as your own biological children.  They can inherit equally. 

Whether step children vs. biological children/adopted children can inherit husband/wife joint property, it's a complicated question depends on which state the property is, how they died, and it has very complicated analysis.