A siblingship test is useful for determining if individuals are full brothers/sisters, half brothers/sisters or unrelated. Whenever the mother(s) is/are known, it is strongly recommended that they be included in the test. Including the mother(s) in the test can increase the combined likelihood ratio ten-fold, where you might see a probability of 98% instead of only 83%.
If two children know they share the same mother and want to see if they also have the same father or, they know they share the same father and would like to see if they both have the same mother, they would meed to be tested as full siblings vs. half siblings
If two children are unsure if they have the same mother and the same father and it’s possible they share neither, they would need to be tested as full siblings vs. unrelated.
If two children have different mothers and want to know if they have the same father or, they know they have different fathers and want to know if they have the same mother, they would need to be tested as half siblings vs. unrelated.
A twin zygosity test can determine whether two siblings are identical or fraternal twins. Testing of the parents is not necessary.