Although there are some minor differences, "guardianship" generally means the same thing as custody: a package which includes all the rights, duties and responsibilities of a parent.
There are minor exceptions and variations here and there- in some States "custody" may not include authority over the child's estate (i.e. their property) whereas unqualified "guardianship" does. Because in the US each State formulates its own laws, this kind of thing can vary depending upon the State the child resides in.