Your Family Tree

I am not entirely sure why the categories are kept distinct, but it seems safe to infer that the question is about your ability to support yourself and those that rely upon you, in connection with an assessment of the risk that you may become a burden on Australian taxpayers.

In effect, if you ceased to be able to provide (out of work, ill, too old etc) and had insufficient savings, how many people would become a burden on the state unless they found a means to support themselves?

1. give detail of dependant children under 18

dependent means they rely on you financially for their support.
children means those that you fathered or mothered (as appropriate), or adopted, or acknowledged as your progeny from around the time of their birth, or for whom a court has decided you are responsible.
under 18 means born less than 18 years earlier than the time you complete the form.

2. give detail of brothers, sisters and other dependent family member

brothers and sisters are those who through blood share one or more parent with you, or are a child, defined as above, of one or other of your parents.
other dependent family member is everyone who is neither a child of yours aged under 18 children nor your brother nor sister, and who relies on you financially for support.

No doubt the courts have refined the definitions above but if more subtle distinction may be relevant then I suggest you consult a lawyer.

To repeat what was a Comment:

A dependant is someone who relies upon you for financial support (so for example might include a partner not married to the provider). A dependent family member is a dependant with familial ties to the provider (eg a spouse perhaps).

Note that in Australian English, dependant (with an a) is a noun, dependent (with an e) is an adjective. American English does not distinguish dependant and dependent and does not spell either with an a. (As kindly pointed out by @Dorothy there is an entire post devoted to exactly what I cover in this note.)